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			<template>
			<div class="chapter" num="6">


			<!-- 第五单元首页 -->
			<div class="page-box" page="160">
			<div v-if="showPageList.indexOf(160) > -1">


			<div class="padding-116">第五单元首页</div>
			<h1 id="a009">
			<img class="img-0" alt="" src="../../assets/images/dy5.jpg" />
			</h1>
			<div class="padding-116">
			<p>
			中华优秀传统文化源远流长、博大精深，是中华文明的智慧结晶.成语“周而复始”出自《汉书·礼乐志》，“精健日月，星辰度理，阴阳五行，周而复始”.在现实世界中，许多事物的运动变化会呈现循环往复、周而复始的规律，我们称这种变化规律为周期性.例如，表针旋转、车轮滚动、物体简谐振动等.这些有规律的变化现象都可用三角函数来刻画.
			</p>
			<p>
			本单元我们将在已学函数概念的基础上，利用函数的思想和方法来学习三角函数的相关内容.三角函数是研究自然界中周期性现象的重要数学工具，它在测量、物理等方面都有着广泛应用.
			</p>
			<p>
			本单元主要将角的概念推广到任意情形，引入弧度制、任意角的三角函数，学习三角函数基本公式及任意角的三角函数的图像和性质.本单元将借助图像理解任意角的三角函数的概念，利用直观想象发现三角函数中数与形之间的联系，会表达其特征与关系；感受用直观想象从具体问题中抽象出数学问题的过程，认识数学中的通性、通法；通过对三角函数具体问题的分析，利用逻辑推理进行三角函数基本公式的推导；初步感知三角函数模型所刻画的简单的周期性函数；提升数学运算、直观想象、逻辑推理和数学抽象等核心素养.
			</p>
			</div>
			</div>
			</div>
			<!-- 目标 -->
			<div class="page-box" page="161">
			<div v-if="showPageList.indexOf(161) > -1">

			<div class="padding-116">目标</div>
			<div class="padding-116">
			<p class="left">
			<img class="inline2" alt="" src="../../assets/images/xxmb.jpg" />
			</p>
			<div class="fieldset">
			<p>1.角的概念推广.</p>
			<p>知道推广角的意义和任意角所在的象限，能识别终边相同的角.</p>
			<p>2.弧度制.</p>
			<p>知道引入弧度制的意义，会进行角度与弧度的换算.</p>
			<p>3.任意角的正弦函数、余弦函数和正切函数.</p>
			<p>
			能根据任意角的三角函数（正弦函数、余弦函数和正切函数）定义，判断三角函数值的符号.
			</p>
			<p>4.同角三角函数的基本关系.</p>
			<p>
			会根据三角函数的定义或借助单位圆，推导同角三角函数的平方关系和商数关系，能进行有关化简和计算.
			</p>
			<p>5.诱导公式.</p>
			<p>知道诱导公式在三角函数求值与化简中的作用.</p>
			<p>6.正弦函数、余弦函数的图像和性质.</p>
			<p>
			会借助代数运算与几何直观，认识正弦函数、余弦函数的图像和性质；
			</p>
			<p>知道运用“五点法”可以画出正弦函数、余弦函数在一个周期上的简图.</p>
			<p>7.已知三角函数值求指定范围的角.</p>
			<p>知道特殊的三角函数值与[0，2<i>π</i>]范围内角的对应关系；</p>
			<p>会用计算工具进行有关的三角计算.</p>
			</div>
			</div>
			</div>
			</div>



			<!-- 155 -->
			<div class="page-box" page="162">
			<div v-if="showPageList.indexOf(162) > -1">
			@@ -32,7 +65,39 @@
			</li>
			</ul>

			<div class="padding-116"></div>
			<div class="padding-116">
			<h2 id="b030">
			5.1 角的概念推广<span class="fontsz1">＞＞＞＞＞＞＞＞</span>
			</h2>
			<h3 id="c048">
			5.1.1 角的概念的推广<span class="fontsz2">＞＞＞</span>
			</h3>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/wttc.jpg" />
			</p>
			<p>
			（1）
			中国跳水队享有奥运“梦之队”的美誉.自1984年到2016年，奥运会跳水项目一共产生了56枚奥运金牌，中国跳水队一共夺得了40枚，约占其中的71.4%.如图5-1（1）
			所示，跳水比赛中有“向前翻腾一周半”和“向后翻腾两周半”的动作，你知道这两个动作分别表示的旋转的角度是多少吗？
			</p>
			<p>
			（2）
			环青海湖国际公路自行车赛是我国规模最大、参赛队伍最多的竞赛，也是世界上海拔最高的国际性竞赛，“绿色、人文、和谐”的竞赛主题倡导体育运动应低碳环保，促进文化交流、人与自然和谐共生.如图5-1（2）
			所示，选手在骑自行车时，自行车车轮在前进和后退的过程中旋转形成的角一样吗？
			</p>
			<p class="center">
			<img class="img-b" alt="" src="../../assets/images/0166-1.jpg" />
			</p>
			<p class="img">图5-1</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>
			<p>
			生活中随处可见超出0°～360°范围的角.问题（1）
			中“向前翻腾一周半”和“向后翻腾两周半”的跳水动作，不仅有超出360°的“一周半”和“两周半”的角，而且旋转的方向也不同，产生的效果也不一样；问题（2）
			中自行车前进时车轮若是逆时针方向旋转，可以旋转几百圈甚至上万圈，后退时车轮则是顺时针方向旋转，其形成的角是不一样的.因此，要准确描述这些现象，就应知道旋转度数和旋转方向，这就需要对角的概念进行推广.
			</p>
			</div>
			</div>
			</div>
			<!-- 156 -->
			@@ -44,7 +109,54 @@
			<li>上册</li>
			</ul>

			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
			</p>
			<p>
			我们规定，一条射线绕其端点按逆时针方向旋转形成的角叫作<b>正角</b>，如图5-2（1）
			所示.按顺时针方向旋转形成的角叫作<b>负角</b>，如图5-2（2）
			所示.如果一条射线没有做任何旋转，就称它形成了一个<b>零角</b>，如图5-2（3）
			所示.
			</p>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0167-1.jpg" />
			</p>
			<p class="img">图5-2</p>
			<p>
			这样我们就把角的概念推广到了<b>任意角</b>，包括正角、负角和零角.
			</p>
			<div class="bk-hzjl">
			<div class="bj1-hzjl">
			<p class="left">
			<img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
			</p>
			</div>
			<p class="block">
			类比实数<i>a</i>与-<i>a</i>互为相反数，角<i>α</i>与角-<i>α</i>是什么关系呢？类比实数减法的“减去一个数等于加上这个数的相反数”，角的减法可以转化为角的加法吗？即<i>α</i>-<i>β</i>=<i>α</i>+（-<i>β</i>）
			成立吗？不妨画图试试.
			</p>
			</div>
			<p>
			为了简便起见，在不引起混淆的前提下，我们把“角<i>α</i>”或“∠<i>α</i>”简记为“<i>α</i>”.今后我们可以用小写希腊字母<i>α</i>，<i>β</i>，<i>γ</i>，…来表示角.
			</p>
			<p>
			在问题（1）
			中，若“向前翻腾一周半”记为<i>α</i>=540°，那么“向后翻腾两周半”则记为<i>α</i>=-900°.在问题（2）
			中，自行车前进或后退，车轮按逆时针方向旋转形成正角，按顺时针方向旋转形成负角.
			</p>
			<p>
			为了方便研究，通常在平面直角坐标系内讨论角.我们将角的顶点与原点重合，角的始边与<i>x</i>轴的非负半轴重合.这样，角的终边在第几象限，就说这个角是第几象限角.
			</p>
			<p>例如，图5-3中的690°角、-210°角分别是第四象限角和第二象限角.</p>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0167-2.jpg" />
			</p>
			<p class="img">图5-3</p>
			<p>
			如果角的终边在坐标轴上，那么就认为这个角不属于任何一个象限（也称界限角）.例如，0°，90°，180°，270°，360°角.
			</p>
			</div>
			</div>
			</div>
			<!-- 157 -->
			@@ -55,25 +167,85 @@
			<p>第五单元三角函数</p>
			</li>
			<li>
			<p><span>157</span></p>
			<p><span>157-158</span></p>
			</li>
			</ul>

			<div class="padding-116"></div>
			<div class="padding-116">
			<p>
			<span class="zt-ls"><b>例1</b></span>　在平面直角坐标系中，分别画出下列各角，并指出它们是第几象限角.
			</p>
			<p class="p-btn" >
			<span>（1） 225°；</span>
			<span class="btn-box" @click="hadleAnswer(0)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer0" >
			<p>
			<span class="zt-ls"><b>解</b></span>（1）
			以<i>x</i>轴的非负半轴为始边，逆时针方向旋转225°，即形成225°角，如图5-4（1）
			所示.因为225°角的终边在第三象限内，所以225°角是第三象限角.
			</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0168-1.jpg" />
			</p>
			<p class="img">图5-4</p>
			</div>
			<p class="p-btn" >
			<span>（2） -300°.</span>
			<span class="btn-box" @click="hadleAnswer(1)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p v-if="isShowAnswer1" >
			<span class="zt-ls"><b>解</b></span>（2）
			以<i>x</i>轴的非负半轴为始边，顺时针方向旋转300°，即形成-300°角，如图5-4（2）
			所示.因为-300°角的终边在第一象限内，所以-300°角是第一象限角.
			</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[164]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
			</div>
			<h3 id="c049">
			5.1.2 终边相同的角<span class="fontsz2">＞＞＞</span>
			</h3>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/wttc.jpg" />
			</p>
			<p>
			如图5-5所示，在平面直角坐标系中，分别画出了-330°，30°，390°角，观察其终边有何联系？-330°，390°与30°在数值上有什么关系？
			</p>
			<p class="center">
			<img class="img-f" alt="" src="../../assets/images/0169-1.jpg" />
			</p>
			<p class="img">图5-5</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>
			<p>
			观察发现，图5-5中-330°，390°与30°角终边相同，并且与30°角终边相同的这些角都可以表示成30°角与<i>k</i>个（<i>k</i>∈<b>Z</b>）周角的和，如
			</p>
			<p class="center">-330°=30°-360°（这里<i>k</i>=-1），</p>
			<p class="center">390°=30°+360°（这里<i>k</i>=1）.</p>
			<p>
			进一步分析可知，与30°角终边相同的所有角都可以表示成30°角与<i>k</i>（<i>k</i>∈<b>Z</b>）个周角的和，因此可用集合<i>S</i>={<i>β</i>\|<i>β</i>=30°+<i>k</i>·360°，<i>k</i>∈<b>Z</b>}表示与30°角终边相同的角.显然，-330°，390°角都是集合<i>S</i>中的元素，30°角也是<i>S</i>中的元素（此时<i>k</i>=0）.反之，集
			</p>
			</div>
			</div>
			</div>
			<!-- 158 -->
			<div class="page-box" page="165">
			<div v-if="showPageList.indexOf(165) > -1">
			<ul class="page-header-odd fl al-end">
			<li>158</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>

			<div class="padding-116"></div>
			</div>
			</div>
			<div class="page-box hidePage" page="165"></div>
			<!-- 159 -->
			<div class="page-box" page="166">
			<div v-if="showPageList.indexOf(166) > -1">
			@@ -82,23 +254,142 @@
			<p>第五单元三角函数</p>
			</li>
			<li>
			<p><span>159</span></p>
			<p><span>159-160</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p>合<i>S</i>中的任何一个元素都与30°角终边相同.</p>
			<p>
			与45°，60°，70°，100°，…角终边相同的角构成的集合又应该如何表达呢？
			</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
			</p>
			<p>
			一般地，所有与<i>α</i>终边相同的角，连同<i>α</i>在内，可以组成一个集合
			</p>
			<p class="center">
			<i>S</i>={<i>β</i>\|<i>β</i>=<i>α</i>+<i>k</i>·360°，<i>k</i>∈<i>Z</i>}.
			</p>
			<p>
			<b>任意的与<i>α</i>终边相同的角都可以表示成<i>α</i>与整数个周角（360°的整数倍）的和.</b>例如，与100°角终边相同的角组成的集合为<i>S</i>={<i>β</i>\|<i>β</i>=100°+<i>k</i>·360°，<i>k</i>∈<b>Z</b>}，当<i>k</i>=0时，<i>β</i>=100°；<i>k</i>=1时，<i>β</i>=460°；<i>k</i>=-1时，<i>β</i>=-260°.
			</p>
			<p>
			<span class="zt-ls"><b>例1</b></span>　在0°～360°内，找出与下列各角终边相同的角，并分别判断它们是第几象限角.
			</p>
			<p class="p-btn" >
			<span>（1） 600°；</span>
			<span class="btn-box" @click="hadleAnswer(2)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p v-if="isShowAnswer2" >
			<span class="zt-ls"><b>解</b></span>（1）因为600°=240°+360°，所以600°角与240°角终边相同，是第三象限角.
			</p>
			<p class="p-btn" >
			<span>（2） -230°；</span>
			<span class="btn-box" @click="hadleAnswer(3)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p v-if="isShowAnswer3" >
			<span class="zt-ls"><b>解</b></span>（2）
			因为-230°=130°-360°，所以-230°角与130°角终边相同，是第二象限角.
			</p>
			<p class="p-btn" >
			<span>（3） -890°.</span>
			<span class="btn-box" @click="hadleAnswer(4)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p v-if="isShowAnswer4" >
			<span class="zt-ls"><b>解</b></span>（3）
			因为-890°=190°-3×360°，所以-890°角与190°角终边相同，是第三象限角.
			</p>
			<p>
			<span class="zt-ls"><b>例2</b></span>　写出下列角的集合.
			</p>
			<p class="p-btn" >
			<span>（1）终边在<i>y</i>轴正半轴上的角的集合；</span>
			<span class="btn-box" @click="hadleAnswer(5)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer5" >
			<p>
			<span class="zt-ls"><b>解</b></span>（1）在0°～360°内，终边在<i>y</i>轴正半轴上的角是90°角，
			</p>
			<p>所以，终边在<i>y</i>轴正半轴上的角的集合是</p>
			<p class="center">
			<i>S</i>1={<i>β</i>\|<i>β</i>=90°+<i>k</i>·360°，<i>k</i>∈<b>Z</b>}.
			</p>
			</div>
			<p class="p-btn" >
			<span>（2）终边在<i>y</i>轴负半轴上的角的集合；</span>
			<span class="btn-box" @click="hadleAnswer(6)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer6" >
			<p><span class="zt-ls"><b>解</b></span>（2）在0°～360°内，终边在<i>y</i>轴负半轴上的角是270°角，</p>
			<p>所以，终边在<i>y</i>轴负半轴上的角的集合是</p>
			<p class="center">
			<i>S</i>2={<i>β</i>\|<i>β</i>=270°+<i>k</i>·360°，<i>k</i>∈<b>Z</b>}.
			</p>
			</div>
			<p class="p-btn" >
			<span>（3）终边在<i>y</i>轴上的角的集合.</span>
			<span class="btn-box" @click="hadleAnswer(7)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer7" >
			<p> <span class="zt-ls"><b>解</b></span>（3）终边在<i>y</i>轴上的角的集合是</p>
			<p><i>S</i>=<i>S</i><sub>1</sub>∪<i>S</i><sub>2</sub></p>
			<p>
			={<i>β</i>\|<i>β</i>=90°+<i>k</i>·360°，<i>k</i>∈<b>Z</b>}∪{<i>β</i>\|<i>β</i>=270°+<i>k</i>·360°，<i>k</i>∈<b>Z</b>}
			</p>
			<p>
			={<i>β</i>\|<i>β</i>=90°+2<i>k</i>·180°，<i>k</i>∈<b>Z</b>}∪{<i>β</i>\|<i>β</i>=90°+（2<i>k</i>+1）·180°，<i>k</i>∈<b>Z</b>}
			</p>
			<p>={<i>β</i>\|<i>β</i>=90°+<i>m</i>·180°，<i>m</i>∈<b>Z</b>}.</p>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[167]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
			</div>
			</div>
			</div>
			</div>

			<!-- 160 -->
			<div class="page-box" page="167">
			<div v-if="showPageList.indexOf(167) > -1">
			<ul class="page-header-odd fl al-end">
			<li>160</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			</div>
			<div class="page-box hidePage" page="167">
			</div>
			<!-- 161 -->
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			@@ -111,8 +402,23 @@
			<p><span>161</span></p>
			</li>
			</ul>

			<div class="padding-116"></div>
			<div class="padding-116">
			<h3 id="c050">习题5.1<span class="fontsz2">＞＞＞</span></h3>
			<div class="bj">
			<examinations :cardList="questionData[168]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
			</div>
			<h2 id="b031">
			5.2 弧度制<span class="fontsz1">＞＞＞＞＞＞＞＞</span>
			</h2>
			<h3 id="c051">
			5.2.1 弧度制的定义<span class="fontsz2">＞＞＞</span>
			</h3>
			<p class="block">
			2016年9月25日，具有我国自主知识产权的世界最大单口径、最灵敏的球面射电望远镜“中国天眼”在贵州平塘落成启用.这个500
			m口径球面射电望远镜
			</p>
			</div>
			</div>
			</div>
			<!-- 162 -->
			@@ -124,7 +430,105 @@
			<li>上册</li>
			</ul>

			<div class="padding-116"></div>
			<div class="padding-116">
			<p>
			主要用于实现巡视宇宙中的中性氢、观测脉冲星等科学目标和空间飞行器测量与通信等应用目标.
			</p>
			<p class="center">
			<img class="img-f" alt="" src="../../assets/images/0172-2.jpg" />
			</p>
			<p>
			在衡量天体之间的距离时，我们可以用光年、米的单位制来度量；对于面积，我们可以用平方米、公顷等不同的单位制来度量；质量可以用千克、吨等不同的单位制来度量.角的大小，我们是否也能用不同的单位制来度量？
			</p>
			<div class="bk">
			<div class="bj1">
			<p class="left">
			<img class="img-gn1" alt="" src="../../assets/images/gn.jpg" />
			</p>
			</div>
			<p class="block">角度制</p>
			<p class="block">弧度制</p>
			<p class="block">弧度</p>
			</div>
			<p>
			我们知道，角可以以度为单位进行度量，把周角的<math display="0">
			<mfrac>
			<mn>1</mn>
			<mn>360</mn>
			</mfrac>
			</math>所对应的圆心角规定为1度的角，记为1°.这种以度为单位来度量角的单位制，叫作<b>角度制</b>.
			</p>
			<p>
			在数学和其他科学研究中，经常使用另一种度量角的单位制——<b>弧度制</b>.
			</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
			</p>
			<p>
			我们规定，长度等于半径的圆弧所对的圆心角叫作1弧度的角，弧度单位用符号rad表示，读作弧度.1弧度的角就记作1
			rad，读作“1弧度”，如图5-6所示.
			</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0173-2.jpg" />
			</p>
			<p class="img">图5-6</p>
			<p>
			根据上述规定可知，在半径为<i>r</i>的圆中，若弧长为<i>l</i>的弧所对的圆心角为<i>α</i>
			rad，则<i>α</i>的大小为
			</p>
			<math display="block">
			<mo stretchy="false">\|</mo>
			<mi>α</mi>
			<mrow>
			<mo stretchy="false">\|</mo>
			</mrow>
			<mo>=</mo>
			<mfrac>
			<mi>l</mi>
			<mi>r</mi>
			</mfrac>
			<mtext>. </mtext>
			</math>
			<p>
			<i>α</i>的正负由<i>α</i>的始边到终边的旋转方向决定，逆时针方向旋转为正，顺时针方向旋转为负.
			</p>
			<p>
			当一个圆的半径为<i>r</i>时，若圆心角∠<i>AOB</i>所对的圆弧长为2<i>r</i>，则∠<i>AOB</i>的弧度数就为<math display="0">
			<mfrac>
			<mrow>
			<mn>2</mn>
			<mi>r</mi>
			</mrow>
			<mi>r</mi>
			</mfrac>
			<mo>=</mo>
			<mn>2</mn>
			<mrow>
			<mi mathvariant="normal">r</mi>
			<mi mathvariant="normal">a</mi>
			<mi mathvariant="normal">d</mi>
			</mrow>
			</math>=2
			rad（如图5-7（1））；若圆心角∠<i>AOB</i>所对的圆弧长为整个圆周长2<i>πr</i>，则∠<i>AOB</i>的弧度数就为<math display="0">
			<mfrac>
			<mrow>
			<mn>2</mn>
			<mi>π</mi>
			<mi>r</mi>
			</mrow>
			<mi>r</mi>
			</mfrac>
			<mo>=</mo>
			<mn>2</mn>
			<mi>π</mi>
			<mrow>
			<mi mathvariant="normal">r</mi>
			<mi mathvariant="normal">a</mi>
			<mi mathvariant="normal">d</mi>
			</mrow>
			</math>（如图5-7（2）），即一个周角的弧度数是2<i>π rad</i>.
			</p>
			</div>
			</div>
			</div>
			<!-- 163 -->
			@@ -138,10 +542,301 @@
			<p><span>163</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<div class="bk">
			<p>360°=2<i>π</i> rad； 180°=<i>π</i> rad；</p>
			<p>
			<math display="0">
			<msup>
			<mn>1</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>=</mo>
			<mfrac>
			<mi>π</mi>
			<mn>180</mn>
			</mfrac>
			<mi>rad</mi>
			<mo>≈</mo>
			<mn>0.01745</mn>
			<mrow>
			<mi mathvariant="normal">r</mi>
			<mi mathvariant="normal">a</mi>
			<mi mathvariant="normal">d</mi>
			</mrow>
			</math>；
			</p>
			<p>
			<math display="0">
			<mn>1</mn>
			<mrow>
			<mi mathvariant="normal">r</mi>
			<mi mathvariant="normal">a</mi>
			<mi mathvariant="normal">d</mi>
			</mrow>
			<mo>=</mo>
			<mfrac>
			<msup>
			<mn>180</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mi>π</mi>
			</mfrac>
			<mo>≈</mo>
			<msup>
			<mn>57.30</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>=</mo>
			<msup>
			<mn>57</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<msup>
			<mn>18</mn>
			<mrow>
			<mi data-mjx-alternate="1" mathvariant="normal">′</mi>
			</mrow>
			</msup>
			</math>.
			</p>
			</div>
			<p class="center">
			<img class="img-b" alt="" src="../../assets/images/0174-3.jpg" />
			</p>
			<p class="img">图5-7</p>
			<p>
			为了简便起见，以弧度为单位表示角的大小时，单位“弧度”或“rad”一般省略不写.例如，1
			rad，<math display="0">
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			<mrow>
			<mi mathvariant="normal">r</mi>
			<mi mathvariant="normal">a</mi>
			<mi mathvariant="normal">d</mi>
			</mrow>
			</math>，0 rad 可简写成1，<math display="0">
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			</math>，0.
			</p>
			<p>
			一般地，正角的弧度数为正数，负角的弧度数为负数，零角的弧度数为0.
			</p>
			<p>
			当形成角的射线旋转一周后继续旋转，就可以得到弧度数大于2<i>π</i>或小于-2<i>π</i>的角.这样就可以得到任意弧度数的角.
			</p>
			<p>
			因此，每一个确定的角都有唯一确定的实数与它对应；反之，每一个确定的实数也都有唯一确定的角与它对应，如图5-8所示.这样，角与实数之间就建立了一一对应的关系.
			</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0174-6.jpg" />
			</p>
			<p class="img">图5-8</p>
			<p class="p-btn" >
			<span><span class="zt-ls"><b>例1</b></span>　把下列各角化为弧度.</span>
			<span class="btn-box" @click="hadleAnswer(8)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p>（1） 30°；（2） -225°；（3） 0°.</p>
			<div v-if="isShowAnswer8" >
			<p>
			<span class="zt-ls"><b>解</b></span>
			</p>
			<p class="left1">
			<math display="">
			<mo stretchy="false">（1）</mo>
			<msup>
			<mn>30</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>=</mo>
			<mn>30</mn>
			<mo>×</mo>
			<mfrac>
			<mi>π</mi>
			<mn>180</mn>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			<mo>.</mo>
			</math>
			</p>
			<p class="left1">
			<math display="">
			<mo stretchy="false">（2）</mo>
			<mo>−</mo>
			<msup>
			<mn>225</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>=</mo>
			<mo>−</mo>
			<mn>225</mn>
			<mo>×</mo>
			<mfrac>
			<mi>π</mi>
			<mn>180</mn>
			</mfrac>
			<mo>=</mo>
			<mo>−</mo>
			<mfrac>
			<mrow>
			<mn>5</mn>
			<mi>π</mi>
			</mrow>
			<mn>4</mn>
			</mfrac>
			<mo>.</mo>
			</math>
			</p>
			<p class="left1">
			<math display="">
			<mo stretchy="false">（3）</mo>
			<msup>
			<mn>0</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>=</mo>
			<mn>0</mn>
			<mo>×</mo>
			<mfrac>
			<mi>π</mi>
			<mn>180</mn>
			</mfrac>
			<mo>=</mo>
			<mn>0</mn>
			<mo>.</mo>
			</math>
			</p>
			</div>
			<p class="p-btn" >
			<span><span class="zt-ls"><b>例2</b></span>　把下列各角化为角度.</span>
			<span class="btn-box" @click="hadleAnswer(9)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p>
			（1）
			<math display="0">
			<mo>−</mo>
			<mfrac>
			<mrow>
			<mi>π</mi>
			</mrow>
			<mn>3</mn>
			</mfrac>
			</math>；（2） 5rad（结果精确到0.01）.
			</p>
			<div v-if="isShowAnswer9" >
			<p>
			<span class="zt-ls"><b>解</b></span>
			</p>
			<p class="left1">
			<math display="">
			<mo stretchy="false">（1）</mo>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>3</mn>
			</mfrac>
			<mo>=</mo>
			<mo>−</mo>
			<mfrac>
			<msup>
			<mn>180</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mn>3</mn>
			</mfrac>
			<mo>=</mo>
			<mo>−</mo>
			<msup>
			<mn>60</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>.</mo>
			</math>
			</p>
			<p class="left1">
			<math display="">
			<mo stretchy="false">（2）</mo>
			<mn>5</mn>
			<mrow>
			<mi mathvariant="normal">r</mi>
			<mi mathvariant="normal">a</mi>
			<mi mathvariant="normal">d</mi>
			</mrow>
			<mo>=</mo>
			<mn>5</mn>
			<mo>×</mo>
			<mfrac>
			<msup>
			<mn>180</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mi>π</mi>
			</mfrac>
			<mo>≈</mo>
			<msup>
			<mn>286.44</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>.</mo>
			</math>
			</p>
			</div>
			<div class="bk mt-60">
			<div class="bj1">
			<p class="left">
			<img class="img-gn1" alt="" src="../../assets/images/tbts.jpg" />
			</p>
			</div>
			<p class="block">
			弧度化角度时,如果式子里有<i>π</i> ,直接把<i>π</i>转化成180°即可.
			</p>
			</div>
			</div>
			</div>
			</div>

			<!-- 164 -->
			<div class="page-box" page="171">
			<div v-if="showPageList.indexOf(171) > -1">
			@@ -150,7 +845,71 @@
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p>
			<span class="zt-ls"><b>例3</b></span>　利用科学计算器，把下列各角进行弧度与角度的互化.（结果精确到0.01）
			</p>
			<p class="p-btn" >
			<span>（1） -5.6；</span>
			<span class="btn-box" @click="hadleAnswer(10)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer10" >
			<p>
			<span class="zt-ls"><b>解</b></span>（1）
			先将科学计算器的精确度设置为0.01，再将科学计算器设置为角度计算模式，科学计算器Ⅰ按<img class="inline" alt=""
			src="../../assets/images/0175-1.jpg" />，科学计算器Ⅱ按<img class="inline" alt=""
			src="../../assets/images/0175-2.jpg" />.之后依次按下列各键.
			</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0175-3.jpg" />
			</p>
			<p>结果显示：</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0175-4.jpg" />
			</p>
			<p>所以　-5.6 <i>rad</i> ≈-320.86°.</p>
			</div>
			<p class="p-btn" >
			<span>（2） 154°13′.</span>
			<span class="btn-box" @click="hadleAnswer(11)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer11" >
			<p>
			<span class="zt-ls"><b>解</b></span>（2）
			先将科学计算器的精确度设置为0.01，再将科学计算器设置为弧度计算模式，科学计算器Ⅰ按<img class="inline" alt=""
			src="../../assets/images/0175-5.jpg" />，科学计算器Ⅱ按<img class="inline" alt=""
			src="../../assets/images/0175-6.jpg" />.之后依次按下列各键.
			</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0175-7.jpg" />
			</p>
			<p>结果显示：</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0175-8.jpg" />
			</p>
			<p>所以　154°13′≈2.69 rad.</p>
			</div>
			<iframe src="https://www.geogebra.org/scientific" frameborder="0" class="iframe-box"></iframe>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[171]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
			</div>
			</div>
			</div>
			</div>
			<!-- 165 -->
			@@ -164,39 +923,494 @@
			<p><span>165</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<h3 id="c052">
			5.2.2 弧长公式、扇形的面积公式<span class="fontsz2">＞＞＞</span>
			</h3>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/wttc.jpg" />
			</p>
			<p>学习了弧度制后，你能推导出弧度制下的弧长和扇形的面积公式吗？</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0176-1.jpg" />
			</p>
			<p class="img">图5-9</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>
			<p>
			如图5-9所示，已知半径为<i>r</i>的圆，设圆心角<i>α</i>=<i>n</i>°，且0°＜<i>α</i>＜360°，<i>α</i>所对的<math display="0">
			<mover>
			<mrow>
			<mi>A</mi>
			<mi>B</mi>
			</mrow>
			<mo>⏜</mo>
			</mover>
			</math>长为<i>l</i>，<i>α</i>所对应的扇形面积为<i>S</i>，则
			</p>
			<p class="center">
			<math display="">
			<mfrac>
			<mi>l</mi>
			<mrow>
			<mn>2</mn>
			<mi>π</mi>
			<mi>r</mi>
			</mrow>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mi>n</mi>
			<mn>360</mn>
			</mfrac>
			</math>，即<math display="0">
			<mi>l</mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mi>n</mi>
			<mi>π</mi>
			<mi>r</mi>
			</mrow>
			<mn>180</mn>
			</mfrac>
			</math>(<i>n</i>°的圆心角所对的弧长为<math display="0">
			<mfrac>
			<mrow>
			<mi>n</mi>
			<mi>π</mi>
			<mi>r</mi>
			</mrow>
			<mn>180</mn>
			</mfrac>
			</math>).
			</p>
			<p class="center">
			<math display="">
			<mfrac>
			<mi>S</mi>
			<mrow>
			<mi>π</mi>
			<msup>
			<mi>r</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			</mrow>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mi>n</mi>
			<mn>360</mn>
			</mfrac>
			</math>，即<math display="0">
			<mi>S</mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mi>n</mi>
			<mi>π</mi>
			<msup>
			<mi>r</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			</mrow>
			<mn>360</mn>
			</mfrac>
			</math>（<i>n</i>°的圆心角所对应的扇形面积为<math display="0">
			<mfrac>
			<mrow>
			<mi>n</mi>
			<mi>π</mi>
			<msup>
			<mi>r</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			</mrow>
			<mn>360</mn>
			</mfrac>
			</math>）.
			</p>
			<p>
			我们知道，弧长<i>l</i>与半径<i>r</i>的比值等于所对圆心角的弧度数，即<i>α</i>，<i>r</i>，<i>l</i>三者之间满足关系式
			</p>
			<math display="block">
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mi>l</mi>
			<mi>r</mi>
			</mfrac>
			<mo>.</mo>
			</math>
			<p>所以，弧长公式为<i>l</i>=<i>αr</i>.</p>
			<p>
			扇形的圆心角为<i>α</i>（0＜<i>α</i>＜2<i>π</i>），圆周角为2<i>π</i>，圆面积为<i>πr</i><sup>2</sup>，所以圆心角为<i>α</i>的扇形面积为
			</p>
			<math display="block">
			<mi>S</mi>
			<mo>=</mo>
			<mfrac>
			<mi>α</mi>
			<mrow>
			<mn>2</mn>
			<mi>π</mi>
			</mrow>
			</mfrac>
			<mo>⋅</mo>
			<mi>π</mi>
			<msup>
			<mi>r</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			<mi>α</mi>
			<msup>
			<mi>r</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			<mi>r</mi>
			<mo>⋅</mo>
			<mi>α</mi>
			<mi>r</mi>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			<mi>r</mi>
			<mi>l</mi>
			<mo>.</mo>
			</math>
			<p>
			将采用角度制表示的和弧度制表示的弧长公式与扇形的面积公式进行对比可知，采用弧度制后弧长公式和扇形的面积公式就更简洁了.
			</p>
			<p class="center">
			<img class="img-d" alt="" src="../../assets/images/0176-11.jpg" />
			</p>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例1</b></span>　截至2021年4月，中国高速公路总里程约为16万千米，位居全球第一.某高速公路转弯处为一弧形高架桥，测得此处公路中线的总长为1
			200 m，该弧形高架桥所对应的圆心角为<math display="0">
			<mfrac>
			<mrow>
			<mn>3</mn>
			<mi>π</mi>
			</mrow>
			<mn>5</mn>
			</mfrac>
			</math>，求该弧形高架桥的转弯半径（结果精确到1 m）.
			</span>
			<span class="btn-box" @click="hadleAnswer(12)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer12" >
			<p>
			<span class="zt-ls"><b>解</b></span> 由题意可知，<i>l</i>=1
			200，<math display="0">
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mn>3</mn>
			<mi>π</mi>
			</mrow>
			<mn>5</mn>
			</mfrac>
			</math>，由<i>l</i>=<i>αr</i>可得
			</p>
			<math display="block">
			<mi>r</mi>
			<mo>=</mo>
			<mfrac>
			<mi>l</mi>
			<mi>α</mi>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mn>1200</mn>
			<mfrac>
			<mrow>
			<mn>3</mn>
			<mi>π</mi>
			</mrow>
			<mn>5</mn>
			</mfrac>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mn>1200</mn>
			<mo>×</mo>
			<mn>5</mn>
			</mrow>
			<mrow>
			<mn>3</mn>
			<mi>π</mi>
			</mrow>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mn>2000</mn>
			<mi>π</mi>
			</mfrac>
			<mo>≈</mo>
			<mn>645</mn>
			<mo stretchy="false">(</mo>
			<mrow>
			<mtext> </mtext>
			<mi mathvariant="normal">m</mi>
			</mrow>
			<mo stretchy="false">)</mo>
			<mo>.</mo>
			</math>
			<p>所以，该弧形高架桥的转弯半径约为645 m.</p>
			</div>
			</div>
			</div>
			</div>

			<!-- 166 -->
			<div class="page-box" page="173">
			<div v-if="showPageList.indexOf(173) > -1">
			<ul class="page-header-odd fl al-end">
			<li>166</li>
			<li>166-167</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>

			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0177-1.jpg" />
			</p>
			<p class="img">图5-10</p>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例2</b></span>　如图5-10所示，要在一块废铁皮上剪出一个扇形，用于制作一个圆锥筒，要求这个扇形的圆心角为60°，半径为90
			cm .请求出这个扇形的弧长与面积.（结果分别精确到0.01 cm和0.01
			cm<sup>2</sup>）
			</span>
			<span class="btn-box" @click="hadleAnswer(13)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer13" >
			<p>
			<span class="zt-ls"><b>解</b></span> 由于<math display="0">
			<msup>
			<mn>60</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>=</mo>
			<mfrac>
			<mi>π</mi>
			<mn>3</mn>
			</mfrac>
			</math>，所以
			</p>
			<math display="block">
			<mtable columnalign="left" columnspacing="1em" rowspacing="4pt">
			<mtr>
			<mtd>
			<mi>l</mi>
			<mo>=</mo>
			<mi>α</mi>
			<mi>r</mi>
			<mo>=</mo>
			<mfrac>
			<mi>π</mi>
			<mn>3</mn>
			</mfrac>
			<mo>×</mo>
			<mn>90</mn>
			<mo>=</mo>
			<mn>30</mn>
			<mi>π</mi>
			<mo>≈</mo>
			<mn>94.26</mn>
			<mo stretchy="false">(</mo>
			<mrow>
			<mtext> </mtext>
			<mi mathvariant="normal">c</mi>
			<mi mathvariant="normal">m</mi>
			</mrow>
			<mo stretchy="false">)</mo>
			</mtd>
			</mtr>
			<mtr>
			<mtd>
			<mi>S</mi>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			<mi>r</mi>
			<mi>l</mi>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			<mo>×</mo>
			<mn>90</mn>
			<mo>×</mo>
			<mn>30</mn>
			<mi>π</mi>
			<mo>≈</mo>
			<mn>4241.70</mn>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mrow>
			<mtext> </mtext>
			<mi mathvariant="normal">c</mi>
			<mi mathvariant="normal">m</mi>
			</mrow>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>.</mo>
			</mtd>
			</mtr>
			</mtable>
			</math>
			<p>
			所以，这个扇形的弧长约为94.26 cm，面积约为4 241.70 cm<sup>2</sup>.
			</p>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[173]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
			</div>
			<h3 id="c053">习题5.2<span class="fontsz2">＞＞＞</span></h3>
			<div class="bj">
			<examinations :cardList="questionData[174]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
			</div>
			<h2 id="b032">
			5.3 任意角的正弦函数、余弦函数和正切函数<span class="fontsz1">＞＞＞＞＞＞＞＞</span>
			</h2>
			<div class="bk">
			<div class="bj1">
			<p class="left">
			<img class="img-gn1" alt="" src="../../assets/images/zshg.jpg" />
			</p>
			</div>
			<p class="block">
			初中我们在Rt△<i>ABC</i>中定义了锐角<i>α</i>的正弦、余弦和正切，如图5-11所示.
			</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0178-7.jpg" />
			</p>
			<p class="img">图5-11</p>
			<p class="block">
			正弦：<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mi>a</mi>
			<mi>c</mi>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mi mathvariant="normal">∠</mi>
			<mi>α</mi>
			<mtext> 的对边 </mtext>
			</mrow>
			<mtext> 斜边 </mtext>
			</mfrac>
			</math>.
			</p>
			<p class="block">
			余弦：<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mi>b</mi>
			<mi>c</mi>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mi mathvariant="normal">∠</mi>
			<mi>α</mi>
			<mtext> 的邻边 </mtext>
			</mrow>
			<mtext> 斜边 </mtext>
			</mfrac>
			</math>.
			</p>
			<p class="block">
			正切：<math display="0">
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mi>a</mi>
			<mi>b</mi>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mi mathvariant="normal">∠</mi>
			<mi>α</mi>
			<mtext> 的对边 </mtext>
			</mrow>
			<mrow>
			<mi mathvariant="normal">∠</mi>
			<mi>α</mi>
			<mtext> 的邻边 </mtext>
			</mrow>
			</mfrac>
			</math>.
			</p>
			</div>
			</div>
			</div>
			</div>

			<!-- 167 -->
			<div class="page-box" page="174">
			<div v-if="showPageList.indexOf(174) > -1">
			<ul class="page-header-box">
			<li>
			<p>第五单元三角函数</p>
			</li>
			<li>
			<p><span>167</span></p>
			</li>
			</ul>

			<div class="padding-116"></div>
			</div>
			</div>

			<div class="page-box hidePage" page="174"></div>
			<!-- 168 -->
			<div class="page-box" page="175">
			<div v-if="showPageList.indexOf(175) > -1">
			@@ -206,10 +1420,232 @@
			<li>上册</li>
			</ul>

			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0179-1.jpg" />
			</p>
			<p class="img">图5-12</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/wttc.jpg" />
			</p>
			<p>
			现在我们将一个锐角<i>α</i>放入平面直角坐标系中，使得顶点与原点重合，始边与<i>x</i>轴的非负半轴重合，如图5-12所示.已知点<i>P</i>（<i>x</i>，<i>y</i>）是锐角<i>α</i>终边上的任意一点，点
			<i>P</i>与原点<i>O</i>的距离<i>OP</i>=<i>r</i>（<i>r</i>＞0），你能利用锐角三角函数的定义计算出锐角<i>α</i>所对应的三角函数值吗？
			</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>
			<p>
			过点<i>P</i>作<i>x</i>轴的垂线，垂足为<i>M</i>，则线段<i>OM</i>的长度为<i>x</i>，线段<i>MP</i>的长度为<i>y</i>.
			</p>
			<p>
			在<i>Rt</i> △<i>OMP</i>中，根据勾股定理可得，<math display="0">
			<mi>r</mi>
			<mo>=</mo>
			<msqrt>
			<msup>
			<mi>x</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo>+</mo>
			<msup>
			<mi>y</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			</msqrt>
			<mo>></mo>
			<mn>0</mn>
			</math>.
			</p>
			<math display="block">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mi>M</mi>
			<mi>P</mi>
			</mrow>
			<mrow>
			<mi>O</mi>
			<mi>P</mi>
			</mrow>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mi>y</mi>
			<mi>r</mi>
			</mfrac>
			<mo>,</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mi>O</mi>
			<mi>M</mi>
			</mrow>
			<mrow>
			<mi>O</mi>
			<mi>P</mi>
			</mrow>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mi>x</mi>
			<mi>r</mi>
			</mfrac>
			<mo>,</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mi>M</mi>
			<mi>P</mi>
			</mrow>
			<mrow>
			<mi>O</mi>
			<mi>M</mi>
			</mrow>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mi>y</mi>
			<mi>x</mi>
			</mfrac>
			<mo>.</mo>
			</math>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
			</p>
			<p>在弧度制下，我们已将<i>α</i>的范围扩展到了全体实数.</p>
			<p class="center">
			<img class="img-f" alt="" src="../../assets/images/0179-4.jpg" />
			</p>
			<p class="img">图5-13</p>
			<p>
			一般地，如图5-13所示，当<i>α</i>为任意角时，点<i>P</i>（<i>x</i>，<i>y</i>）是<i>α</i>的终边上异于原点的任意一点，点<i>P</i>到原点的距离为<math
			display="0">
			<mi>r</mi>
			<mo>=</mo>
			<msqrt>
			<msup>
			<mi>x</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo>+</mo>
			<msup>
			<mi>y</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			</msqrt>
			</math>.我们仍然将<i>α</i>的正弦、余弦、正切分别定义如下.
			</p>
			<math display="block">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mi>y</mi>
			<mi>r</mi>
			</mfrac>
			<mo>,</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mi>x</mi>
			<mi>r</mi>
			</mfrac>
			<mo>,</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mi>y</mi>
			<mi>x</mi>
			</mfrac>
			<mo stretchy="false">(</mo>
			<mi>x</mi>
			<mo>≠</mo>
			<mn>0</mn>
			<mo stretchy="false">)</mo>
			<mo>.</mo>
			</math>
			<p>注意：当<i>α</i>的终边不在<i>y</i>轴上时，tan<i>α</i>才有意义.</p>
			<p>
			对于每一个确定的<i>α</i>，其正弦、余弦及正切都分别对应一个确定的比值，因此，正弦、余弦及正切都是以<i>α</i>为自变量的函数，分别叫作正弦函数、余弦函数及正切函数.
			</p>
			<p>
			当点<i>P</i>的横坐标<i>x</i>=0时，<i>α</i>的终边在<i>y</i>轴上，此时<math display="0">
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo>+</mo>
			<mi>k</mi>
			<mi>π</mi>
			<mo stretchy="false">(</mo>
			<mi>k</mi>
			<mo>∈</mo>
			<mrow>
			<mi mathvariant="bold">Z</mi>
			</mrow>
			<mo stretchy="false">)</mo>
			</math>，<math display="0">
			<mfrac>
			<mi>y</mi>
			<mi>x</mi>
			</mfrac>
			<mo>=</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			</math>无意义.除此之外，对于确定的<i>α</i>，三个函数都有意义.
			</p>
			<p>我们将正弦函数、余弦函数和正切函数统称为三角函数，通常记为：</p>
			<p><b>正弦函数</b> <i>y</i>=sin <i>x</i>，<i>x</i>∈<b>R</b>；</p>
			<p><b>余弦函数</b> <i>y</i>=cos <i>x</i>，<i>x</i>∈<b>R</b>；</p>
			<p>
			<b>正切函数</b> <i>y</i>=tan <i>x</i>，<math display="0">
			<mi>x</mi>
			<mo>≠</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo>+</mo>
			<mi>k</mi>
			<mi>π</mi>
			<mo stretchy="false">(</mo>
			<mi>k</mi>
			<mo>∈</mo>
			<mrow>
			<mi mathvariant="bold">Z</mi>
			</mrow>
			<mo stretchy="false">)</mo>
			</math>.
			</p>
			</div>
			</div>
			</div>

			<!-- 169 -->
			<div class="page-box" page="176">
			<div v-if="showPageList.indexOf(176) > -1">
			@@ -221,10 +1657,146 @@
			<p><span>169</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例1</b></span>　如图5-14所示，已知<i>α</i>的终边经过点 <i>P</i>（3，-4），
			求sin<i>α</i>，cos<i>α</i>，tan<i>α</i>的值.
			</span>
			<span class="btn-box" @click="hadleAnswer(14)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0180-3.jpg" />
			</p>
			<p class="img">图5-14</p>
			<div v-if="isShowAnswer36" >
			<p>
			<span class="zt-ls"><b>解</b></span>
			由已知有<i>x</i>=3，<i>y</i>=-4，
			</p>
			<p>则</p>
			<math display="block">
			<mi>r</mi>
			<mo>=</mo>
			<msqrt>
			<msup>
			<mn>3</mn>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo>+</mo>
			<mo stretchy="false">(</mo>
			<mo>−</mo>
			<mn>4</mn>
			<msup>
			<mo stretchy="false">)</mo>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			</msqrt>
			<mo>=</mo>
			<mn>5</mn>
			<mo>.</mo>
			</math>
			<p>于是</p>
			<math display="block">
			<mtable columnalign="left" columnspacing="1em" rowspacing="4pt">
			<mtr>
			<mtd>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mi>y</mi>
			<mi>r</mi>
			</mfrac>
			<mo>=</mo>
			<mo>−</mo>
			<mfrac>
			<mn>4</mn>
			<mn>5</mn>
			</mfrac>
			<mo>,</mo>
			</mtd>
			</mtr>
			<mtr>
			<mtd>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mi>x</mi>
			<mi>r</mi>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mn>3</mn>
			<mn>5</mn>
			</mfrac>
			<mo>,</mo>
			</mtd>
			</mtr>
			<mtr>
			<mtd>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mi>y</mi>
			<mi>x</mi>
			</mfrac>
			<mo>=</mo>
			<mo>−</mo>
			<mfrac>
			<mn>4</mn>
			<mn>3</mn>
			</mfrac>
			<mo>.</mo>
			</mtd>
			</mtr>
			</mtable>
			</math>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[176]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/wttc.jpg" />
			</p>
			<p>
			从<i>α</i>的正弦、余弦和正切的定义与实例可知，任意角的正弦值、余弦值和正切值在不同的象限有不同的符号.下面我们来研究各个象限内，任意角的正弦值、余弦值和正切值的符号的规律.
			</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>
			<p>
			以第二象限角为例，根据任意角的正弦、余弦和正切的定义，试分析它们在第二象限的符号情况.
			</p>
			<p>
			因为<i>α</i>的终边在第二象限，任取终边上异于原点的一点<i>P</i>（<i>x</i>，<i>y</i>），有
			</p>
			<p class="center">
			<i>x</i>＜0， <i>y</i>＞0， <i>OP</i>= <i>r</i>＞0.
			</p>
			<p>根据任意角的正弦、余弦和正切的定义可知，</p>
			</div>
			</div>
			</div>

			<!-- 170 -->
			<div class="page-box" page="177">
			<div v-if="showPageList.indexOf(177) > -1">
			@@ -233,7 +1805,80 @@
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p>
			（1）<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mi>y</mi>
			<mi>r</mi>
			</mfrac>
			<mo>></mo>
			<mn>0</mn>
			</math>；
			</p>
			<p>
			（2）<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mi>x</mi>
			<mi>r</mi>
			</mfrac>
			<mo><</mo>
			<mn>0</mn>
			</math>；
			</p>
			<p>
			（3）<math display="0">
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mi>y</mi>
			<mi>x</mi>
			</mfrac>
			<mo><</mo>
			<mn>0</mn>
			</math>.
			</p>
			<p>所以，可以得出第二象限各值的符号，见表5-2.</p>
			<p class="img">表5-2</p>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0181-4.jpg" />
			</p>
			<p>同理，可得出其他象限内各值的符号.</p>
			<p>
			一般地，<i>α</i>为任意角，<i>P</i>（<i>x</i>，<i>y</i>）为<i>α</i>终边上异于原点的任意一点，点
			<i>P</i>与原点<i>O</i>的距离<i>OP</i>=<i>r</i>.因为<i>r</i>＞0，由定义可知，
			</p>
			<p><b>正弦值的符号与点<i>P</i>的纵坐标<i>y</i>的符号相同；</b></p>
			<p><b>余弦值的符号与点<i>P</i>的横坐标<i>x</i>的符号相同；</b></p>
			<p>
			<b>正切值的符号与点<i>P</i>的纵坐标与横坐标的比值</b><math display="0">
			<mfrac>
			<mi>y</mi>
			<mi>x</mi>
			</mfrac>
			</math><b>的符号相同.</b>
			</p>
			<p>
			将点<i>P</i>（<i>x</i>，<i>y</i>）的坐标与各象限角的正弦值、余弦值和正切值的符号列表，如表5-3所示.
			</p>
			<p class="img">表5-3</p>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0181-6.jpg" />
			</p>
			<p>
			为了便于记忆，我们将sin<i>α</i>，cos<i>α</i>，tan<i>α</i>的符号标在各象限内，如图5-15所示.
			</p>
			</div>
			</div>
			</div>
			<!-- 171 -->
			@@ -247,11 +1892,161 @@
			<p><span>171</span></p>
			</li>
			</ul>

			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="center">
			<img class="img-b" alt="" src="../../assets/images/0182-1.jpg" />
			</p>
			<p class="img">图5-15</p>
			<p>
			<span class="zt-ls"><b>例2</b></span>　确定下列各三角函数值的符号.
			</p>
			<p class="p-btn" >
			<span>（1） sin（-210°）；</span>
			<span class="btn-box" @click="hadleAnswer(15)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer15" >
			<p>
			<span class="zt-ls"><b>解</b></span>（1）因为-210°是第二象限角，所以
			</p>
			<p class="center">sin（-210°）＞0.</p>
			</div>
			<p class="p-btn" >
			<span>（2） tan760°；</span>
			<span class="btn-box" @click="hadleAnswer(16)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer16" >
			<p>
			<span class="zt-ls"><b>解</b></span>（2）
			因为760°=40°+2×360°，可知760°角与40°角的终边相同，是第一象限角，所以
			</p>
			<p class="center">tan 760°＞0.</p>
			</div>
			<p class="p-btn" >
			<span>
			（3）
			<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>17</mn>
			<mi>π</mi>
			</mrow>
			<mn>12</mn>
			</mfrac>
			</math>.
			</span>
			<span class="btn-box" @click="hadleAnswer(17)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer17" >
			<p>
			<span class="zt-ls"><b>解</b></span>（3）由<math display="0">
			<mfrac>
			<mrow>
			<mn>17</mn>
			<mi>π</mi>
			</mrow>
			<mn>12</mn>
			</mfrac>
			<mo>=</mo>
			<mi>π</mi>
			<mo>+</mo>
			<mfrac>
			<mn>5</mn>
			<mn>12</mn>
			</mfrac>
			<mi>π</mi>
			</math>，可看出<math display="0">
			<mi>π</mi>
			<mo><</mo>
			<mi>π</mi>
			<mo>+</mo>
			<mfrac>
			<mrow>
			<mn>5</mn>
			<mi>π</mi>
			</mrow>
			<mn>12</mn>
			</mfrac>
			<mo><</mo>
			<mi>π</mi>
			<mo>+</mo>
			<mfrac>
			<mrow>
			<mn>6</mn>
			<mi>π</mi>
			</mrow>
			<mn>12</mn>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mn>3</mn>
			<mi>π</mi>
			</mrow>
			<mn>2</mn>
			</mfrac>
			</math>，是第三象限角，
			</p>
			<p>所以</p>
			<math display="block">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>17</mn>
			<mi>π</mi>
			</mrow>
			<mn>12</mn>
			</mfrac>
			<mo><</mo>
			<mn>0</mn>
			</math>
			</div>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例3</b></span>　根据sin <i>α</i>＞0，且cos <i>α</i>＜0，确定<i>α</i>是第几象限角.
			</span>
			<span class="btn-box" @click="hadleAnswer(18)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p v-if="isShowAnswer18">
			<span class="zt-ls"><b>解</b></span> 因为sin
			<i>α</i>＞0，所以<i>α</i>的终边在第一或第二象限或<i>y</i>轴的正半轴上；又因为cos<i>α</i>＜0，所以<i>α</i>的终边在第二或第三象限或<i>x</i>轴的负半轴上.因此，<i>α</i>为第二象限角.
			</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[178]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
			</div>
			</div>
			</div>
			</div>

			<!-- 172 -->
			<div class="page-box" page="179">
			<div v-if="showPageList.indexOf(179) > -1">
			@@ -261,7 +2056,90 @@
			<li>上册</li>
			</ul>

			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="center">
			<img style="width: 24%" alt="" src="../../assets/images/0183-1.jpg" />
			</p>
			<p class="img">图5-16</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/wttc.jpg" />
			</p>
			<p>
			如图5-16所示，两个三角板上有几个特殊的锐角：30°，45°，60°.初中已研究了它们对应的正弦值、余弦值和正切值.现将角的范围进行了推广，已经在平面直角坐标系中研究了各象限角的正弦值、余弦值和正切值的符号分布规律.对于在平面直角坐标系中不属于任何象限的特殊角，如0°，90°，180°，270°等，它们的正弦值、余弦值和正切值又是多少？以180°为例，试求出它的正弦值、余弦值和正切值.
			</p>
			<p class="center">
			<img class="img-f" alt="" src="../../assets/images/0183-2.jpg" />
			</p>
			<p class="img">图5-17</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>
			<p>
			在平面直角坐标系中，180°角的终边正好与<i>x</i>轴的负半轴重合，如图5-17所示.以坐标原点为圆心、半径为单位长度的圆（简称单位圆）与<i>x</i>轴交于点<i>P</i>（-1，0），于是有
			</p>
			<p class="center"><i>x</i>=-1，<i>y</i>=0，<i>r</i>=1.</p>
			<p>根据任意角的正弦、余弦和正切的定义可知，</p>
			<math display="block">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<mn>180</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>=</mo>
			<mfrac>
			<mi>y</mi>
			<mi>r</mi>
			</mfrac>
			<mo>=</mo>
			<mn>0</mn>
			<mo>;</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<mn>180</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>=</mo>
			<mfrac>
			<mi>x</mi>
			<mi>r</mi>
			</mfrac>
			<mo>=</mo>
			<mo>−</mo>
			<mn>1</mn>
			<mo>;</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<mn>180</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>=</mo>
			<mfrac>
			<mi>y</mi>
			<mi>x</mi>
			</mfrac>
			<mo>=</mo>
			<mn>0</mn>
			<mo>.</mo>
			</math>
			<p><b>类比归纳</b></p>
			<p>
			一般地，取单位圆与坐标轴的交点就可以得到0°，90°，180°和270°等特殊角的正弦值、余弦值和正切值，如表5-4所示.
			</p>
			<p class="img">表5-4</p>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0183-4.jpg" />
			</p>
			<p>表中360°角与0°角的终边相同，对应的三角函数值也相同.</p>
			</div>
			</div>
			</div>
			<!-- 173 -->
			@@ -272,27 +2150,217 @@
			<p>第五单元三角函数</p>
			</li>
			<li>
			<p><span>173</span></p>
			<p><span>173-174</span></p>
			</li>
			</ul>
			<div class="padding-116">
			<p>
			</p>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例4</b></span>　求5sin180°-4sin90°+2tan180°-7sin270°的值.
			</span>
			<span class="btn-box" @click="hadleAnswer(19)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer19" >
			<p>
			<span class="zt-ls"><b>解</b></span> 5sin 180°-4sin 90°+2 tan
			180°-7sin 270°
			</p>
			<p>=5×0-4×1+2×0-7×（-1）</p>
			<p>=3.</p>
			</div>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例5</b></span>　求<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			<mo>−</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>3</mn>
			</mfrac>
			<mo>+</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>π</mi>
			<mo>−</mo>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>3</mn>
			<mi>π</mi>
			</mrow>
			<mn>2</mn>
			</mfrac>
			</math>的值.
			</span>
			<span class="btn-box" @click="hadleAnswer(20)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer20" >

			<div class="padding-116"></div>
			<p>
			<span class="zt-ls"><b>解</b></span>
			</p>
			<p class="left1">
			<math display="">
			<mtable displaystyle="true"
			columnalign="right left right left right left right left right left right left"
			columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" rowspacing="3pt">
			<mtr>
			<mtd></mtd>
			<mtd>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			<mo>−</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>3</mn>
			</mfrac>
			<mo>+</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>π</mi>
			<mo>−</mo>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>3</mn>
			<mi>π</mi>
			</mrow>
			<mn>2</mn>
			</mfrac>
			</mtd>
			</mtr>
			<mtr>
			<mtd>
			<mo>=</mo>
			</mtd>
			<mtd>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			<mo>−</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			<mo>+</mo>
			<mo stretchy="false">(</mo>
			<mo>−</mo>
			<mn>1</mn>
			<mo stretchy="false">)</mo>
			<mo>−</mo>
			<mo stretchy="false">(</mo>
			<mo>−</mo>
			<mn>1</mn>
			<mo stretchy="false">)</mo>
			</mtd>
			</mtr>
			<mtr>
			<mtd>
			<mo>=</mo>
			</mtd>
			<mtd>
			<mn>0</mn>
			<mo>.</mo>
			</mtd>
			</mtr>
			</mtable>
			</math>
			</p>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[180] ? questionData[180][1] : []" :hideCollect="true"
			sourceType="json" inputBc="#d3edfa" v-if="questionData"></examinations>
			</div>
			<h3 id="c054">习题5.3<span class="fontsz2">＞＞＞</span></h3>
			<div class="bj">
			<examinations :cardList="questionData[180] ? questionData[180][2] : []" :hideCollect="true"
			sourceType="json" inputBc="#d3edfa" v-if="questionData"></examinations>
			</div>
			<h2 id="b033">
			5.4 同角三角函数的基本关系<span class="fontsz1">＞＞＞＞＞＞＞＞</span>
			</h2>
			<p>
			在上一节，我们学习了三角函数的定义以及在各个象限的符号，那么同一个角的三角函数值之间是否存在某种关系呢？
			</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0185-4.jpg" />
			</p>
			<p class="img">图5-18</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>
			<p>
			我们知道，在平面直角坐标系中，单位圆是以原点为圆心、单位长度为半径的圆.下面我们利用单位圆来研究同角三角函数的基本关系.如图5-18所示，已知点<i>P</i>（<i>x</i>，<i>y</i>）是角<i>α</i>的终边与单位圆的交点.过点<i>P</i>作<i>x</i>轴的垂线，垂足为<i>M</i>，则△<i>OMP</i>是直角三角形，且<i>OM</i>=｜<i>x</i>｜，<i>PM</i>=｜<i>y</i>｜，<i>OP</i>=<i>r</i>=1.
			</p>
			<p>根据正弦、余弦和正切的定义可知，在单位圆上，</p>
			<math display="block">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mi>y</mi>
			<mo>;</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mi>x</mi>
			<mo>;</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mi>y</mi>
			<mi>x</mi>
			</mfrac>
			<mo>,</mo>
			<mi>x</mi>
			<mo>≠</mo>
			<mn>0</mn>
			<mo>.</mo>
			</math>
			<p>
			在Rt △<i>OPM</i>中，由勾股定理有<i>OM</i><sup>2</sup>+<i>PM</i><sup>2</sup>=<i>OP</i><sup>2</sup>，
			</p>
			</div>
			</div>
			</div>

			<!-- 174 -->
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			<ul class="page-header-odd fl al-end">
			<li>174</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>

			<div class="padding-116"></div>
			</div>
			</div>

			<div class="page-box hidePage" page="181"></div>
			<!-- 175 -->
			<div class="page-box" page="182">
			<div v-if="showPageList.indexOf(182) > -1">
			@@ -301,25 +2369,992 @@
			<p>第五单元三角函数</p>
			</li>
			<li>
			<p><span>175</span></p>
			<p><span>175-176</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p>即<i>x</i><sup>2</sup>+<i>y</i><sup>2</sup>=1，</p>
			<p>所以sin<sup>2</sup><i>α</i>+cos<sup>2</sup><i>α</i>=1.</p>
			<p>显然，当<i>α</i>的终边与坐标轴重合时，这个公式也成立.</p>
			<p>
			根据正切的定义，当<math display="0">
			<mi>α</mi>
			<mo>≠</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo>+</mo>
			<mi>k</mi>
			<mi>π</mi>
			<mo stretchy="false">(</mo>
			<mi>k</mi>
			<mo>∈</mo>
			<mrow>
			<mi mathvariant="bold">Z</mi>
			</mrow>
			<mo stretchy="false">)</mo>
			</math>时，
			</p>
			<math display="block">
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			</mrow>
			<mrow>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			</mrow>
			</mfrac>
			<mo>.</mo>
			</math>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
			</p>
			<p>一般地，可以得到同角三角函数的基本关系式.</p>
			<p>
			<b>（1）平方关系：</b>sin<sup>2</sup><i>α</i>+cos<sup>2</sup><i>α</i>=1.
			</p>
			<p>
			<b>（2）商数关系：</b><math display="0">
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			</mrow>
			<mrow>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			</mrow>
			</mfrac>
			</math>.
			</p>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例1</b></span>　已知<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mn>3</mn>
			<mn>5</mn>
			</mfrac>
			</math>，且<i>α</i>是第四象限角，求sin<i>α</i>，tan<i>α</i>的值.
			</span>
			<span class="btn-box" @click="hadleAnswer(21)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer21" >
			<p>
			<span class="zt-ls"><b>解</b></span> 因为
			<i>α</i>是第四象限角，所以sin<i>α</i>＜0 .
			</p>
			<math display="block">
			<mtable columnspacing="1em" rowspacing="4pt">
			<mtr>
			<mtd>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mo>−</mo>
			<msqrt>
			<mn>1</mn>
			<mo>−</mo>
			<msup>
			<mi>cos</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			</msqrt>
			<mo>=</mo>
			<mo>−</mo>
			<msqrt>
			<mn>1</mn>
			<mo>−</mo>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mn>3</mn>
			<mn>5</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			</msqrt>
			<mo>=</mo>
			<mo>−</mo>
			<mfrac>
			<mn>4</mn>
			<mn>5</mn>
			</mfrac>
			<mo>,</mo>
			</mtd>
			</mtr>
			<mtr>
			<mtd>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			</mrow>
			<mrow>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			</mrow>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mo>−</mo>
			<mfrac>
			<mn>4</mn>
			<mn>5</mn>
			</mfrac>
			</mrow>
			<mfrac>
			<mn>3</mn>
			<mn>5</mn>
			</mfrac>
			</mfrac>
			<mo>=</mo>
			<mo>−</mo>
			<mfrac>
			<mn>4</mn>
			<mn>3</mn>
			</mfrac>
			<mo>.</mo>
			</mtd>
			</mtr>
			</mtable>
			</math>
			</div>
			<div class="bk">
			<div class="bj1">
			<p class="left">
			<img class="img-gn1" alt="" src="../../assets/images/tbts.jpg" />
			</p>
			</div>
			<p class="block">
			根据sin<sup>2</sup><i>α</i>+cos<sup>2</sup><i>α</i>=1，可得<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<msqrt>
			<mn>1</mn>
			<mo>−</mo>
			<msup>
			<mi>cos</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			</msqrt>
			</math>或<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mo>−</mo>
			<msqrt>
			<mn>1</mn>
			<mo>−</mo>
			<msup>
			<mi>cos</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			</msqrt>
			</math>.其开方后的符号是由正弦值的象限符号来确定的.同理，开方后余弦值的符号也一样.
			</p>
			</div>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例2</b></span>　已知<math display="0">
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mn>12</mn>
			<mn>5</mn>
			</mfrac>
			</math>，且<i>α</i>是第三象限角，求sin <i>α</i>，cos <i>α</i>的值.
			</span>
			<span class="btn-box" @click="hadleAnswer(22)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer22" >
			<p>
			<span class="zt-ls"><b>解</b></span>
			</p>
			<math display="block">
			<mtext> 由 </mtext>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mn>12</mn>
			<mn>5</mn>
			</mfrac>
			<mtext> 得, </mtext>
			<mfrac>
			<mrow>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			</mrow>
			<mrow>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			</mrow>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mn>12</mn>
			<mn>5</mn>
			</mfrac>
			<mtext>, 即 </mtext>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mn>12</mn>
			<mn>5</mn>
			</mfrac>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mtext>. </mtext>
			</math>
			<p>把①代入</p>
			<math display="block">
			<msup>
			<mi>sin</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>+</mo>
			<msup>
			<mi>cos</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mn>1</mn>
			<mo>,</mo>
			</math>
			<p class="right">①</p>
			<p>得</p>
			<math display="block">
			<mtable columnspacing="1em" rowspacing="4pt">
			<mtr>
			<mtd>
			<msup>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mn>12</mn>
			<mn>5</mn>
			</mfrac>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo>+</mo>
			<msup>
			<mi>cos</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mn>1</mn>
			<mo>,</mo>
			</mtd>
			</mtr>
			<mtr>
			<mtd>
			<mfrac>
			<mn>169</mn>
			<mn>25</mn>
			</mfrac>
			<msup>
			<mi>cos</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mn>1</mn>
			<mo>,</mo>
			</mtd>
			</mtr>
			<mtr>
			<mtd>
			<msup>
			<mi>cos</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mn>25</mn>
			<mn>169</mn>
			</mfrac>
			<mo>.</mo>
			</mtd>
			</mtr>
			</mtable>
			</math>
			<p>因为<i>α</i>是第三象限角，所以cos<i>α</i>＜0.</p>
			<p>
			所以<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mo>−</mo>
			<mfrac>
			<mn>5</mn>
			<mn>13</mn>
			</mfrac>
			</math>.
			</p>
			<p>
			把<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mo>−</mo>
			<mfrac>
			<mn>5</mn>
			<mn>13</mn>
			</mfrac>
			</math>代入①式，得
			</p>
			<math display="block">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mn>12</mn>
			<mn>5</mn>
			</mfrac>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mn>12</mn>
			<mn>5</mn>
			</mfrac>
			<mo>×</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mfrac>
			<mn>5</mn>
			<mn>13</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<mo>−</mo>
			<mfrac>
			<mn>12</mn>
			<mn>13</mn>
			</mfrac>
			<mo>.</mo>
			</math>
			</div>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例3</b></span>　求证sin<sup>4</sup><i>α</i>-cos<sup>4</sup><i>α</i>=2sin
			<sup>2</sup><i>α</i>-1.
			</span>
			<span class="btn-box" @click="hadleAnswer(23)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer23" >
			<p>
			<b>证明</b> sin<sup>4</sup><i>α</i>-cos<sup>4</sup><i>α</i>=（sin
			<sup>2</sup><i>α</i>+cos<sup>2</sup><i>α</i>）（sin<sup>2</sup><i>α</i>-cos<sup>2</sup><i>α</i>）
			</p>
			<p>=sin<sup>2</sup><i>α</i>-cos<sup>2</sup><i>α</i></p>
			<p>=sin<sup>2</sup><i>α</i>-（1-sin<sup>2</sup><i>α</i>）</p>
			<p>=2sin<sup>2</sup><i>α</i>-1.</p>
			</div>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例4</b></span>　化简<math display="0">
			<mfrac>
			<mrow>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			<mo>−</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			</mrow>
			<mrow>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			<mo>−</mo>
			<mn>1</mn>
			</mrow>
			</mfrac>
			</math>.
			</span>
			<span class="btn-box" @click="hadleAnswer(24)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer24" >
			<p>
			<span class="zt-ls"><b>解</b></span>
			</p>
			<math display="block">
			<mo>由</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			</mrow>
			<mrow>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			</mrow>
			</mfrac>
			<mo>=</mo>
			<mo>−</mo>
			<mn>3</mn>
			<mo>,</mo>
			<mo>得</mo>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			<mo>=</mo>
			<mo>−</mo>
			<mn>3</mn>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			<mo>.</mo>
			<mtable displaystyle="true" columnalign="right left right left right left right left right left right left"
			columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" rowspacing="3pt">
			<mtr>
			<mtd>
			<mfrac>
			<mrow>
			<mn>4</mn>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			<mo>−</mo>
			<mn>2</mn>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			</mrow>
			<mrow>
			<mn>5</mn>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			<mo>+</mo>
			<mn>3</mn>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			</mrow>
			</mfrac>
			</mtd>
			<mtd>
			<mi></mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mn>4</mn>
			<mo stretchy="false">(</mo>
			<mo>−</mo>
			<mn>3</mn>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			<mo stretchy="false">)</mo>
			<mo>−</mo>
			<mn>2</mn>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			</mrow>
			<mrow>
			<mn>5</mn>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			<mo>+</mo>
			<mn>3</mn>
			<mo stretchy="false">(</mo>
			<mo>−</mo>
			<mn>3</mn>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			<mo stretchy="false">)</mo>
			</mrow>
			</mfrac>
			</mtd>
			</mtr>
			<mtr>
			<mtd></mtd>
			<mtd>
			<mi></mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mo>−</mo>
			<mn>14</mn>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			</mrow>
			<mrow>
			<mo>−</mo>
			<mn>4</mn>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			</mrow>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mn>7</mn>
			<mn>2</mn>
			</mfrac>
			<mo>.</mo>
			</mtd>
			</mtr>
			</mtable>
			</math>
			</div>
			<div class="bk mt-60">
			<div class="bj1">
			<p class="left">
			<img class="img-gn1" alt="" src="../../assets/images/tbts.jpg" />
			</p>
			</div>
			<p class="block">
			方法一的运算思路是由正弦函数、余弦函数变化为正切函数求出结果，我们简称为“弦化切”；方法二的运算思路是由正切函数变化为正弦函数和余弦函数的关系后求出结果，我们简称为“切化弦”.
			</p>
			</div>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例5</b></span>　已知tan<i>θ</i>=-3，求<math display="0">
			<mfrac>
			<mrow>
			<mn>4</mn>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			<mo>−</mo>
			<mn>2</mn>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			</mrow>
			<mrow>
			<mn>5</mn>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			<mo>+</mo>
			<mn>3</mn>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			</mrow>
			</mfrac>
			</math>的值.
			</span>
			<span class="btn-box" @click="hadleAnswer(25)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer25" >
			<p>
			<span class="zt-ls"><b>解</b></span> 方法一：显然cos <i>θ</i>≠0，
			</p>
			<p class="left1">
			<math display="">
			<mfrac>
			<mrow>
			<mn>4</mn>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			<mo>−</mo>
			<mn>2</mn>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			</mrow>
			<mrow>
			<mn>5</mn>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			<mo>+</mo>
			<mn>3</mn>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			</mrow>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mfrac>
			<mrow>
			<mn>4</mn>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			</mrow>
			<mrow>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			</mrow>
			</mfrac>
			<mo>−</mo>
			<mfrac>
			<mrow>
			<mn>2</mn>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			</mrow>
			<mrow>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			</mrow>
			</mfrac>
			</mrow>
			<mrow>
			<mfrac>
			<mrow>
			<mn>5</mn>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			</mrow>
			<mrow>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			</mrow>
			</mfrac>
			<mo>+</mo>
			<mfrac>
			<mrow>
			<mn>3</mn>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			</mrow>
			<mrow>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			</mrow>
			</mfrac>
			</mrow>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mn>4</mn>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			<mo>−</mo>
			<mn>2</mn>
			</mrow>
			<mrow>
			<mn>5</mn>
			<mo>+</mo>
			<mn>3</mn>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			</mrow>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mn>4</mn>
			<mo>×</mo>
			<mo stretchy="false">(</mo>
			<mo>−</mo>
			<mn>3</mn>
			<mo stretchy="false">)</mo>
			<mo>−</mo>
			<mn>2</mn>
			</mrow>
			<mrow>
			<mn>5</mn>
			<mo>+</mo>
			<mn>3</mn>
			<mo>×</mo>
			<mo stretchy="false">(</mo>
			<mo>−</mo>
			<mn>3</mn>
			<mo stretchy="false">)</mo>
			</mrow>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mn>7</mn>
			<mn>2</mn>
			</mfrac>
			<mo>.</mo>
			</math>
			</p>
			<p>方法二：</p>
			<p class="left1">
			<math display="">
			<mo>由</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			</mrow>
			<mrow>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			</mrow>
			</mfrac>
			<mo>=</mo>
			<mo>−</mo>
			<mn>3</mn>
			<mo>,</mo>
			<mo>得</mo>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			<mo>=</mo>
			<mo>−</mo>
			<mn>3</mn>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			<mo>.</mo>
			</math>
			</p>
			<p class="left1">
			<math display="">
			<mtable displaystyle="true"
			columnalign="right left right left right left right left right left right left"
			columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" rowspacing="3pt">
			<mtr>
			<mtd>
			<mfrac>
			<mrow>
			<mn>4</mn>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			<mo>−</mo>
			<mn>2</mn>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			</mrow>
			<mrow>
			<mn>5</mn>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			<mo>+</mo>
			<mn>3</mn>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			</mrow>
			</mfrac>
			</mtd>
			<mtd>
			<mi></mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mn>4</mn>
			<mo stretchy="false">(</mo>
			<mo>−</mo>
			<mn>3</mn>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			<mo stretchy="false">)</mo>
			<mo>−</mo>
			<mn>2</mn>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			</mrow>
			<mrow>
			<mn>5</mn>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			<mo>+</mo>
			<mn>3</mn>
			<mo stretchy="false">(</mo>
			<mo>−</mo>
			<mn>3</mn>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			<mo stretchy="false">)</mo>
			</mrow>
			</mfrac>
			</mtd>
			</mtr>
			<mtr>
			<mtd></mtd>
			<mtd>
			<mi></mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mo>−</mo>
			<mn>14</mn>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			</mrow>
			<mrow>
			<mo>−</mo>
			<mn>4</mn>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>θ</mi>
			</mrow>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mn>7</mn>
			<mn>2</mn>
			</mfrac>
			<mo>.</mo>
			</mtd>
			</mtr>
			</mtable>
			</math>
			</p>
			</div>
			</div>
			</div>
			</div>

			<!-- 176 -->
			<div class="page-box" page="183">
			<div v-if="showPageList.indexOf(183) > -1">
			<ul class="page-header-odd fl al-end">
			<li>176</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			</div>
			<div class="page-box hidePage" page="183">
			</div>

			<!-- 177 -->
			<div class="page-box" page="184">
			<div v-if="showPageList.indexOf(184) > -1">
			@@ -331,11 +3366,22 @@
			<p><span>177</span></p>
			</li>
			</ul>

			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[184] ? questionData[184][1] : []" :hideCollect="true"
			sourceType="json" inputBc="#d3edfa" v-if="questionData"></examinations>
			</div>
			<h3 id="c055">习题5.4<span class="fontsz2">＞＞＞</span></h3>
			<div class="bj">
			<examinations :cardList="questionData[184] ? questionData[184][2] : []" :hideCollect="true"
			sourceType="json" inputBc="#d3edfa" v-if="questionData"></examinations>
			</div>
			</div>
			</div>
			</div>

			<!-- 178 -->
			<div class="page-box" page="185">
			<div v-if="showPageList.indexOf(185) > -1">
			@@ -344,10 +3390,170 @@
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<h2 id="b034">
			5.5 诱导公式<span class="fontsz1">＞＞＞＞＞＞＞＞</span>
			</h2>
			<p>
			我们知道，图像的对称性是函数性质（如奇偶性）的重要几何特征.在上一节，我们借助单位圆推导了同角三角函数的基本关系式.下面，我们继续利用在平面直角坐标系中关于原点中心对称的单位圆，推导三角函数的诱导公式.
			</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/wttc.jpg" />
			</p>
			<p>
			我们知道，<math display="0">
			<mfrac>
			<mi>α</mi>
			<mn>3</mn>
			</mfrac>
			</math>和<math display="0">
			<mfrac>
			<mrow>
			<mn>7</mn>
			<mi>π</mi>
			</mrow>
			<mn>3</mn>
			</mfrac>
			</math>（<math display="0">
			<mfrac>
			<mrow>
			<mn>7</mn>
			<mi>π</mi>
			</mrow>
			<mn>3</mn>
			</mfrac>
			</math>可写为<math display="0">
			<mfrac>
			<mi>π</mi>
			<mn>3</mn>
			</mfrac>
			<mo>+</mo>
			<mn>2</mn>
			<mi>π</mi>
			</math>）所对应的角是终边相同的角.想一想，<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>3</mn>
			</mfrac>
			</math>与<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>7</mn>
			<mi>π</mi>
			</mrow>
			<mn>3</mn>
			</mfrac>
			</math>，<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>3</mn>
			</mfrac>
			</math>与<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>7</mn>
			<mi>π</mi>
			</mrow>
			<mn>3</mn>
			</mfrac>
			</math>之间有什么关系？
			</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0189-9.jpg" />
			</p>
			<p class="img">图5-19</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>
			<p>
			在平面直角坐标系中，由于<math display="0">
			<mfrac>
			<mi>π</mi>
			<mn>3</mn>
			</mfrac>
			</math>和<math display="0">
			<mfrac>
			<mrow>
			<mn>7</mn>
			<mi>π</mi>
			</mrow>
			<mn>3</mn>
			</mfrac>
			</math>所对应的角的终边相同，所以由三角函数的定义可知，<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>3</mn>
			</mfrac>
			<mo>=</mo>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>7</mn>
			<mi>π</mi>
			</mrow>
			<mn>3</mn>
			</mfrac>
			</math>，<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>3</mn>
			</mfrac>
			<mo>=</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>7</mn>
			<mi>π</mi>
			</mrow>
			<mn>3</mn>
			</mfrac>
			</math>.
			</p>
			<p>
			如图5-19所示，角<i>α</i>的终边与单位圆的交点为<i>P</i>（cos<i>α</i>，sin<i>α</i>），终边继续旋转2<i>πk</i>（<i>k</i>∈<b>Z</b>）后，点<i>P</i>（cos<i>α</i>，sin<i>α</i>）又回到原来的位置，所以各三角函数值并不发生变化.
			</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
			</p>
			<p>
			我们知道，所有与<i>α</i>终边相同的角，连同<i>α</i>在内，可以组成一个集合
			</p>
			<p class="center">
			<i>S</i>={<i>β</i>\|<i>β</i>=<i>α</i>+2<i>kπ</i>，<i>k</i>∈<b>Z</b>}.
			</p>
			<p>
			由三角函数的定义可知，角<i>α</i>+2<i>kπ</i>（<i>k</i>∈<b>Z</b>）与角<i>α</i>的同名三角函数的值相等（“同名”指同为正弦、余弦或正切，下同）.于是，当<i>k</i>∈<b>Z</b>时，
			</p>
			<div class="bj">
			<p class="center">
			有sin（<i>α</i>+2<i>kπ</i>）=sin <i>α</i>（<i>k</i>∈<b>Z</b>）；
			</p>
			<p class="center">
			cos（<i>α</i>+2<i>kπ</i>）=cos<i>α</i>（<i>k</i>∈<i>Z</i>）；
			公式一
			</p>
			<p class="center">
			tan（<i>α</i>+2<i>kπ</i>）=tan<i>α</i>（<i>k</i>∈<b>Z</b>）.
			</p>
			</div>
			<p>即终边相同的角同名三角函数值相等.</p>
			</div>
			</div>
			</div>

			<!-- 179 -->
			<div class="page-box" page="186">
			<div v-if="showPageList.indexOf(186) > -1">
			@@ -359,8 +3565,214 @@
			<p><span>179</span></p>
			</li>
			</ul>

			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="p-btn" >
			<span><span class="zt-ls"><b>例1</b></span>　求下列三角函数的值.</span>
			<span class="btn-box" @click="hadleAnswer(26)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p>
			（1）
			<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>13</mn>
			<mi>π</mi>
			</mrow>
			<mn>6</mn>
			</mfrac>
			</math>；（2）
			<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mfrac>
			<mrow>
			<mn>5</mn>
			<mi>π</mi>
			</mrow>
			<mn>3</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>；（3） tan 405°.
			</p>
			<div v-if="isShowAnswer26" >
			<p>
			<span class="zt-ls"><b>解</b></span>（1）<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>13</mn>
			<mi>π</mi>
			</mrow>
			<mn>6</mn>
			</mfrac>
			<mo>=</mo>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			<mo>+</mo>
			<mn>2</mn>
			<mi>π</mi>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</math>；
			</p>
			<p>
			（2）
			<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mfrac>
			<mrow>
			<mn>5</mn>
			<mi>π</mi>
			</mrow>
			<mn>3</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mi>π</mi>
			<mn>3</mn>
			</mfrac>
			<mo>−</mo>
			<mn>2</mn>
			<mi>π</mi>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>3</mn>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</math>；
			</p>
			<p>（3） tan405°=tan（45°+360°）=tan45°=1.</p>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[186]" :hideCollect="true" sourceType="json" v-if="questionData">
			</examinations>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/gcsk.jpg" />
			</p>
			<p>
			如图5-20所示，<math display="0">
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			</math>和<math display="0">
			<mfrac>
			<mrow>
			<mn>7</mn>
			<mi>π</mi>
			</mrow>
			<mn>6</mn>
			</mfrac>
			</math>（<math display="0">
			<mfrac>
			<mrow>
			<mn>7</mn>
			<mi>π</mi>
			</mrow>
			<mn>6</mn>
			</mfrac>
			</math>可写为<math display="0">
			<mi>π</mi>
			<mo>+</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			</math>）所对应的角的终边关于坐标原点对称.想一想，<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			</math>与<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>7</mn>
			<mi>π</mi>
			</mrow>
			<mn>6</mn>
			</mfrac>
			</math>，<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			</math>与<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>7</mn>
			<mi>π</mi>
			</mrow>
			<mn>6</mn>
			</mfrac>
			</math>之间有什么关系？
			</p>
			<p class="center">
			<img class="img-f" alt="" src="../../assets/images/0190-25.jpg" />
			</p>
			<p class="img">图5-20</p>
			</div>
			</div>
			</div>
			<!-- 180 -->
			@@ -371,7 +3783,168 @@
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>
			<p>
			如图5-20所示，<math display="0">
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			</math>和<math display="0">
			<mfrac>
			<mrow>
			<mn>7</mn>
			<mi>π</mi>
			</mrow>
			<mn>6</mn>
			</mfrac>
			</math>所对应的角的终边与单位圆的交点分别是点<i>P</i>与点<i>P</i>′.根据对称性可知，它们的横坐标与纵坐标都互为相反数.
			</p>
			<p>由此得到</p>
			<math display="block">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			<mo>=</mo>
			<mo>−</mo>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>7</mn>
			<mi>π</mi>
			</mrow>
			<mn>6</mn>
			</mfrac>
			<mo>=</mo>
			<mo>−</mo>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mi>π</mi>
			<mo>+</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>,</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			<mo>=</mo>
			<mo>−</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>7</mn>
			<mi>π</mi>
			</mrow>
			<mn>6</mn>
			</mfrac>
			<mo>=</mo>
			<mo>−</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mi>π</mi>
			<mo>+</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>.</mo>
			</math>
			<p>
			如图5-21所示，设单位圆与任意角<i>α</i>，π+<i>α</i>的终边分别相交于点<i>P</i>和<i>P</i>′，则点<i>P</i>和<i>P</i>′关于原点中心对称.如果点<i>P</i>的坐标是（cos
			<i>α</i>，sin
			<i>α</i>），那么点<i>P</i>′的坐标应该是（-cos<i>α</i>，-sin<i>α</i>）.又由于点<i>P</i>′作为角π+<i>α</i>的终边与单位圆的交点，其坐标应该是（cos（π+<i>α</i>），sin（π+<i>α</i>）），由此得到
			</p>
			<p class="center">
			cos（π+<i>α</i>）=-cos<i>α</i>，sin（π+<i>α</i>）=-sin<i>α</i>.
			</p>
			<p>由同角三角函数的关系式知</p>
			<math display="block">
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mo stretchy="false">(</mo>
			<mi>π</mi>
			<mo>+</mo>
			<mi>α</mi>
			<mo stretchy="false">)</mo>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mo stretchy="false">(</mo>
			<mi>π</mi>
			<mo>+</mo>
			<mi>α</mi>
			<mo stretchy="false">)</mo>
			</mrow>
			<mrow>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mo stretchy="false">(</mo>
			<mi>π</mi>
			<mo>+</mo>
			<mi>α</mi>
			<mo stretchy="false">)</mo>
			</mrow>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mo>−</mo>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			</mrow>
			<mrow>
			<mo>−</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			</mrow>
			</mfrac>
			<mo>=</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>.</mo>
			</math>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0191-5.jpg" />
			</p>
			<p class="img">图5-21</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
			</p>
			<p>
			与任意角<i>α</i>的终边关于原点中心对称的角π+<i>α</i>的正弦函数、余弦函数和正切函数的计算公式如下.
			</p>
			<div class="bj">
			<p class="center">　sin（π+<i>α</i>）=-sin<i>α</i>；</p>
			<p class="center">　　　　cos（π+<i>α</i>）=-cos<i>α</i>；公式二</p>
			<p class="center">tan（π+<i>α</i>）=tan<i>α</i>.</p>
			</div>
			</div>
			</div>
			</div>
			<!-- 181 -->
			@@ -385,7 +3958,284 @@
			<p><span>181</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="p-btn" >
			<span><span class="zt-ls"><b>例2</b></span>　求下列三角函数的值. </span>
			<span class="btn-box" @click="hadleAnswer(27)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p>
			（1） sin 225°；（2）
			<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>4</mn>
			<mi>π</mi>
			</mrow>
			<mn>3</mn>
			</mfrac>
			</math>；（3） tan 570°.
			</p>
			<div v-if="isShowAnswer27" >
			<p>
			<span class="zt-ls"><b>解</b></span>（1）<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<mn>225</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>=</mo>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mn>180</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>+</mo>
			<msup>
			<mn>45</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<mo>−</mo>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<mn>45</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>=</mo>
			<mo>−</mo>
			<mfrac>
			<msqrt>
			<mn>2</mn>
			</msqrt>
			<mn>2</mn>
			</mfrac>
			</math>；
			</p>
			<p>
			（2）<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>4</mn>
			<mi>π</mi>
			</mrow>
			<mn>3</mn>
			</mfrac>
			<mo>=</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mi>π</mi>
			<mo>+</mo>
			<mfrac>
			<mi>π</mi>
			<mn>3</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<mo>−</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>3</mn>
			</mfrac>
			<mo>=</mo>
			<mo>−</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</math>；
			</p>
			<p>
			（3）<math display="0">
			<mtable displaystyle="true"
			columnalign="right left right left right left right left right left right left"
			columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" rowspacing="3pt">
			<mtr>
			<mtd>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<mn>570</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			</mtd>
			<mtd>
			<mi></mi>
			<mo>=</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mn>210</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>+</mo>
			<msup>
			<mn>360</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<mn>210</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>=</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mn>180</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>+</mo>
			<msup>
			<mn>30</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<mn>30</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			</mtd>
			</mtr>
			<mtr>
			<mtd></mtd>
			<mtd>
			<mi></mi>
			<mo>=</mo>
			<mfrac>
			<msqrt>
			<mn>3</mn>
			</msqrt>
			<mn>3</mn>
			</mfrac>
			</mtd>
			</mtr>
			</mtable>
			</math>
			</p>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[188]" :hideCollect="true" sourceType="json" v-if="questionData">
			</examinations>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/gcsk.jpg" />
			</p>
			<p>
			如图5-22所示，<math display="0">
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			</math>和<math display="0">
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			</math>所对应的角的终边关于<i>x</i>轴对称.想一想，<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			</math>与<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>，<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			</math>与<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>之间有什么关系？
			</p>
			<p class="center">
			<img class="img-f" alt="" src="../../assets/images/0192-23.jpg" />
			</p>
			<p class="img">图5-22</p>
			</div>
			</div>
			</div>
			<!-- 182 -->
			@@ -396,7 +4246,382 @@
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>
			<p>
			如图5-22所示，<math display="0">
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			</math>和<math display="0">
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			</math>所对应的角的终边与单位圆的交点分别是点<i>P</i>与点<i>P</i>′.根据对称性可知，点<i>P</i>与点<i>P</i>′的横坐标相同、纵坐标互为相反数.
			</p>
			<p>
			由此得到<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			<mo>=</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>，<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			<mo>=</mo>
			<mo>−</mo>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>.
			</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0193-5.jpg" />
			</p>
			<p class="img">图5-23</p>
			<p>
			如图5-23所示，设单位圆与任意角<i>α</i>，-<i>α</i>的终边分别相交于点<i>P</i>和点<i>P</i>′，则点<i>P</i>与点<i>P</i>′关于<i>x</i>轴对称.如果点<i>P</i>的坐标是（cos<i>α</i>，sin<i>α</i>），那么点<i>P</i>′的坐标是（cos<i>α</i>，-sin<i>α</i>）.由于点<i>P</i>′作为角-<i>α</i>的终边与单位圆的交点，其坐标应该是（cos（-<i>α</i>），sin（-<i>α</i>）），于是得到
			</p>
			<p class="center">
			cos（-<i>α</i>）=cos<i>α</i>，sin（-<i>α</i>）=-sin<i>α</i>.
			</p>
			<p>由同角三角函数的关系式知</p>
			<math display="block">
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mo stretchy="false">(</mo>
			<mo>−</mo>
			<mi>α</mi>
			<mo stretchy="false">)</mo>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mo stretchy="false">(</mo>
			<mo>−</mo>
			<mi>α</mi>
			<mo stretchy="false">)</mo>
			</mrow>
			<mrow>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mo stretchy="false">(</mo>
			<mo>−</mo>
			<mi>α</mi>
			<mo stretchy="false">)</mo>
			</mrow>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mo>−</mo>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			</mrow>
			<mrow>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			</mrow>
			</mfrac>
			<mo>=</mo>
			<mo>−</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>.</mo>
			</math>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
			</p>
			<p>
			与任意角<i>α</i>的终边关于<i>x</i>轴对称的角-<i>α</i>的正弦函数、余弦函数和正切函数的计算公式如下.
			</p>
			<div class="bj">
			<p class="center">sin（-<i>α</i>）=-sin<i>α</i>；</p>
			<p class="center">cos（-<i>α</i>）=cos<i>α</i>；公式三</p>
			<p class="center">tan（-<i>α</i>）=-tan<i>α</i>.</p>
			</div>
			<div class="bk">
			<div class="bj1">
			<p class="left">
			<img class="img-gn1" alt="" src="../../assets/images/tbts.jpg" />
			</p>
			</div>
			<p class="block">
			利用公式三，可以把负角的三角函数转化为正角的三角函数.
			</p>
			</div>
			<p class="p-btn" >
			<span><span class="zt-ls"><b>例3</b></span>　求下列三角函数的值.</span>
			<span class="btn-box" @click="hadleAnswer(28)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p>
			（1） sin（-45°）；（2） cos（-390°）；（3）
			<math display="0">
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mo stretchy="false">(</mo>
			<mo>−</mo>
			<mfrac>
			<mrow>
			<mn>16</mn>
			<mi>π</mi>
			</mrow>
			<mn>3</mn>
			</mfrac>
			<mo stretchy="false">)</mo>
			</math>.
			</p>
			<div v-if="isShowAnswer28" >
			<p>
			<span class="zt-ls"><b>解</b></span>
			</p>
			<p class="left1">
			<math display="">
			<mo stretchy="false">（1）</mo>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<msup>
			<mn>45</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<mo>−</mo>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<mn>45</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>=</mo>
			<mo>−</mo>
			<mfrac>
			<msqrt>
			<mn>2</mn>
			</msqrt>
			<mn>2</mn>
			</mfrac>
			<mo>;</mo>
			</math>
			</p>
			<p class="left1">
			<math display="">
			<mo stretchy="false">（2）</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<msup>
			<mn>390</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<mn>390</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>=</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mn>30</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>+</mo>
			<msup>
			<mn>360</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<mn>30</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>=</mo>
			<mfrac>
			<msqrt>
			<mn>3</mn>
			</msqrt>
			<mn>2</mn>
			</mfrac>
			<mo>;</mo>
			</math>
			</p>
			<p class="left1">
			<math display="">
			<mo stretchy="false">（3）</mo>
			<mtable displaystyle="true"
			columnalign="right left right left right left right left right left right left"
			columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" rowspacing="3pt">
			<mtr>
			<mtd>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mfrac>
			<mrow>
			<mn>16</mn>
			<mi>π</mi>
			</mrow>
			<mn>3</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</mtd>
			<mtd>
			<mi></mi>
			<mo>=</mo>
			<mo>−</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>16</mn>
			<mi>π</mi>
			</mrow>
			<mn>3</mn>
			</mfrac>
			<mo>=</mo>
			<mo>−</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mrow>
			<mn>4</mn>
			<mi>π</mi>
			</mrow>
			<mn>3</mn>
			</mfrac>
			<mo>+</mo>
			<mn>4</mn>
			<mi>π</mi>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<mo>−</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>4</mn>
			<mi>π</mi>
			</mrow>
			<mn>3</mn>
			</mfrac>
			</mtd>
			</mtr>
			<mtr>
			<mtd></mtd>
			<mtd>
			<mi></mi>
			<mo>=</mo>
			<mo>−</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mi>π</mi>
			<mo>+</mo>
			<mfrac>
			<mi>π</mi>
			<mn>3</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<mo>−</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>3</mn>
			</mfrac>
			<mo>=</mo>
			<mo>−</mo>
			<msqrt>
			<mn>3</mn>
			</msqrt>
			</mtd>
			</mtr>
			</mtable>
			</math>
			</p>
			</div>
			</div>
			</div>
			</div>
			<!-- 183 -->
			@@ -410,7 +4635,85 @@
			<p><span>183</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[190]" :hideCollect="true" sourceType="json" v-if="questionData">
			</examinations>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/gcsk.jpg" />
			</p>
			<p>
			如图5-24所示，<i>α</i>和π-<i>α</i>所对应的角的终边关于<i>y</i>轴对称.想一想，sin<i>α</i>与sin（π-<i>α</i>），cos<i>α</i>与cos（π-<i>α</i>）之间有什么关系？
			</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0194-14.jpg" />
			</p>
			<p class="img">图5-24</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>
			<p>
			如图5-24所示，设单位圆与角<i>α</i>，π-<i>α</i>的终边分别相交于点<i>P</i>和点<i>P</i>′，则点<i>P</i>与点<i>P</i>′关于<i>y</i>轴对称.如果点<i>P</i>的坐标是（cos<i>α</i>，sin<i>α</i>），那么点<i>P</i>′的坐标是（-cos<i>α</i>，sin<i>α</i>）.由于点<i>P</i>′作为角π-<i>α</i>的终边与单位圆的交点，其坐标应该是（cos（π-<i>α</i>），sin（π-<i>α</i>）），
			</p>
			<p class="center">
			cos（π-<i>α</i>）=-cos<i>α</i>， sin（π-<i>α</i>）=sin<i>α</i>.
			</p>
			<p>由同角三角函数的关系式知</p>
			<math display="block">
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mo stretchy="false">(</mo>
			<mi>π</mi>
			<mo>−</mo>
			<mi>α</mi>
			<mo stretchy="false">)</mo>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mo stretchy="false">(</mo>
			<mi>π</mi>
			<mo>−</mo>
			<mi>α</mi>
			<mo stretchy="false">)</mo>
			</mrow>
			<mrow>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mo stretchy="false">(</mo>
			<mi>π</mi>
			<mo>−</mo>
			<mi>α</mi>
			<mo stretchy="false">)</mo>
			</mrow>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			</mrow>
			<mrow>
			<mo>−</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			</mrow>
			</mfrac>
			<mo>=</mo>
			<mo>−</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>.</mo>
			</math>
			</div>
			</div>
			</div>
			<!-- 184 -->
			@@ -421,10 +4724,446 @@
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
			</p>
			<p>
			与任意角<i>α</i>的终边关于<i>y</i>轴对称的角π-<i>α</i>的正弦函数、余弦函数和正切函数的计算公式如下.
			</p>
			<div class="bj">
			<p class="center">sin（π-<i>α</i>）=sin<i>α</i>；</p>
			<p class="center">cos（π-<i>α</i>）=-cos<i>α</i>；公式四</p>
			<p class="center">tan（π-<i>α</i>）=-tan<i>α</i>.</p>
			</div>
			<p>
			公式一至公式四统称为三角函数的诱导公式.利用这些公式可以把任意角的三角函数转化为锐角三角函数.
			</p>
			<p class="p-btn" >
			<span><span class="zt-ls"><b>例4</b></span>　求下列三角函数的值.</span>
			<span class="btn-box" @click="hadleAnswer(29)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p>
			（1） cos 135°；（2）
			<math display="0">
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>8</mn>
			<mi>π</mi>
			</mrow>
			<mn>3</mn>
			</mfrac>
			</math>；（3）
			<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>11</mn>
			<mi>π</mi>
			</mrow>
			<mn>4</mn>
			</mfrac>
			</math>.
			</p>
			<div v-if="isShowAnswer29" >
			<p>
			<span class="zt-ls"><b>解</b></span>
			</p>
			<p class="left1">
			<math display="">
			<mo stretchy="false">（1）</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<mn>135</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>=</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<msup>
			<mn>180</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>−</mo>
			<msup>
			<mn>45</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<mo>−</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<mn>45</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>=</mo>
			<mo>−</mo>
			<mfrac>
			<msqrt>
			<mn>2</mn>
			</msqrt>
			<mn>2</mn>
			</mfrac>
			<mo>;</mo>
			</math>
			</p>
			<p class="left1">
			<math display="">
			<mo stretchy="false">（2）</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>8</mn>
			<mi>π</mi>
			</mrow>
			<mn>3</mn>
			</mfrac>
			<mo>=</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mrow>
			<mn>2</mn>
			<mi>π</mi>
			</mrow>
			<mn>3</mn>
			</mfrac>
			<mo>+</mo>
			<mn>2</mn>
			<mi>π</mi>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>2</mn>
			<mi>π</mi>
			</mrow>
			<mn>3</mn>
			</mfrac>
			<mo>=</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mi>π</mi>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>3</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<mo>−</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>3</mn>
			</mfrac>
			<mo>=</mo>
			<mo>−</mo>
			<msqrt>
			<mn>3</mn>
			</msqrt>
			<mo>;</mo>
			</math>
			</p>
			<p class="left1">
			<math display="">
			<mo stretchy="false">（3）</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>11</mn>
			<mi>π</mi>
			</mrow>
			<mn>4</mn>
			</mfrac>
			<mo>=</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mrow>
			<mn>3</mn>
			<mi>π</mi>
			</mrow>
			<mn>4</mn>
			</mfrac>
			<mo>+</mo>
			<mn>2</mn>
			<mi>π</mi>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>3</mn>
			<mi>π</mi>
			</mrow>
			<mn>4</mn>
			</mfrac>
			<mo>=</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mi>π</mi>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>4</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<mo>−</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>4</mn>
			</mfrac>
			<mo>=</mo>
			<mo>−</mo>
			<mfrac>
			<msqrt>
			<mn>2</mn>
			</msqrt>
			<mn>2</mn>
			</mfrac>
			<mo>.</mo>
			</math>
			</p>
			</div>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例5</b></span>　化简：<math display="0">
			<mfrac>
			<mrow>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mo stretchy="false">(</mo>
			<mn>2</mn>
			<mi>π</mi>
			<mo>−</mo>
			<mi>α</mi>
			<mo stretchy="false">)</mo>
			<mo>⋅</mo>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mo stretchy="false">(</mo>
			<mn>3</mn>
			<mi>π</mi>
			<mo>+</mo>
			<mi>α</mi>
			<mo stretchy="false">)</mo>
			</mrow>
			<mrow>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mo stretchy="false">(</mo>
			<mo>−</mo>
			<mi>π</mi>
			<mo>+</mo>
			<mi>α</mi>
			<mo stretchy="false">)</mo>
			<mo>⋅</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mo stretchy="false">(</mo>
			<mn>3</mn>
			<mi>π</mi>
			<mo>−</mo>
			<mi>α</mi>
			<mo stretchy="false">)</mo>
			<mo>⋅</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mo stretchy="false">(</mo>
			<mo>−</mo>
			<mi>α</mi>
			<mo>−</mo>
			<mi>π</mi>
			<mo stretchy="false">)</mo>
			</mrow>
			</mfrac>
			</math>
			</span>
			<span class="btn-box" @click="hadleAnswer(30)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer30" >
			<p>
			<span class="zt-ls"><b>解</b></span>
			</p>
			<p class="left1">
			<math display="">
			<mtable displaystyle="true"
			columnalign="right left right left right left right left right left right left"
			columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" rowspacing="3pt">
			<mtr>
			<mtd>
			<mtext> 原式 </mtext>
			</mtd>
			<mtd>
			<mi></mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mo>−</mo>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>⋅</mo>
			<mo stretchy="false">(</mo>
			<mo>−</mo>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo stretchy="false">)</mo>
			</mrow>
			<mrow>
			<mo>−</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo stretchy="false">(</mo>
			<mo>−</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo stretchy="false">)</mo>
			<mo stretchy="false">(</mo>
			<mo>−</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo stretchy="false">)</mo>
			</mrow>
			</mfrac>
			</mtd>
			</mtr>
			<mtr>
			<mtd></mtd>
			<mtd>
			<mi></mi>
			<mo>=</mo>
			<mo>−</mo>
			<mfrac>
			<mrow>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>⋅</mo>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			</mrow>
			<mrow>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>⋅</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>⋅</mo>
			<mfrac>
			<mrow>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			</mrow>
			<mrow>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			</mrow>
			</mfrac>
			</mrow>
			</mfrac>
			</mtd>
			</mtr>
			<mtr>
			<mtd></mtd>
			<mtd>
			<mi></mi>
			<mo>=</mo>
			<mo>−</mo>
			<mfrac>
			<mrow>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			</mrow>
			<mrow>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			</mrow>
			</mfrac>
			<mo>=</mo>
			<mo>−</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>.</mo>
			</mtd>
			</mtr>
			</mtable>
			</math>
			</p>
			</div>
			<p><b>归纳总结</b></p>
			<p>
			利用诱导公式，把任意角的三角函数值转化为锐角的三角函数值的一般步骤为：
			</p>
			<p class="center">
			<img class="img-d" alt="" src="../../assets/images/0195-6.jpg" />
			</p>
			</div>
			</div>
			</div>

			<!-- 185 -->
			<div class="page-box" page="192">
			<div v-if="showPageList.indexOf(192) > -1">
			@@ -433,24 +5172,194 @@
			<p>第五单元三角函数</p>
			</li>
			<li>
			<p><span>185</span></p>
			<p><span>185-186</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p>
			事实上，以上步骤体现了将未知转化为已知的化归思想.利用公式一至公式四，按上述步骤解决了求三角函数值这个重要而困难的问题.现在，由于计算工具的便捷使用，对于三角函数的“求值”已不是问题，但其中的思想方法在解决三角函数的各种问题中却依然有重要的作用.
			</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[192]" :hideCollect="true" sourceType="json" v-if="questionData">
			</examinations>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/wttc.jpg" />
			</p>
			<p>
			前面我们探究了求特殊角的三角函数值的方法，而对于不是特殊角的三角函数值又该如何求值呢？使用计算工具就能很容易地解决这个问题.
			</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>
			<p>
			利用科学计算器的<img class="inline" alt="" src="../../assets/images/0196-13.jpg" />键，可以方便地计算任意角的三角函数值.
			</p>
			<p>
			主要步骤如下：设置精确度→设置模式（角度制或弧度制）→按键<img class="inline" alt="" src="../../assets/images/0196-14.jpg" />（或键<img
			class="inline" alt="" src="../../assets/images/0196-15.jpg" />）→输入角的大小→按键<img class="inline" alt=""
			src="../../assets/images/0196-16.jpg" />显示结果.
			</p>
			<p>
			<span class="zt-ls"><b>例6</b></span>　利用科学计算器计算.（结果精确到0.01）
			</p>
			<p class="p-btn" >
			<span>（1） sin 63°52′41″；</span>
			<span class="btn-box" @click="hadleAnswer(31)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer31" >
			<p>
			<span class="zt-ls"><b>解</b></span>（1）
			先将精确度设置为0.01，再将科学计算器设置为角度计算模式，然后依次按下列各键：
			</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0197-1.jpg" />
			</p>
			<p>结果显示：</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0197-2.jpg" />
			</p>
			<p>所以 sin 63°52′41″≈0.90.</p>
			</div>
			<p class="p-btn" >
			<span>
			（2）<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>4</mn>
			<mi>π</mi>
			</mrow>
			<mn>3</mn>
			</mfrac>
			</math>；
			</span>
			<span class="btn-box" @click="hadleAnswer(32)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer32" >
			<p>
			<span class="zt-ls"><b>解</b></span>（2）
			先将精确度设置为0.01，再将科学计算器设置为弧度计算模式，然后依次按下列各键：
			</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0197-3.jpg" />
			</p>
			<p>结果显示：</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0197-4.jpg" />
			</p>
			<p>
			所以
			<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>4</mn>
			<mi>π</mi>
			</mrow>
			<mn>3</mn>
			</mfrac>
			<mo>=</mo>
			<mo>−</mo>
			<mn>0.50</mn>
			<mo>.</mo>
			</math>
			</p>
			</div>
			<p class="p-btn" >
			<span>
			（3）
			<math display="0">
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mfrac>
			<mrow>
			<mn>6</mn>
			<mi>π</mi>
			</mrow>
			<mn>5</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>.
			</span>
			<span class="btn-box" @click="hadleAnswer(33)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer33" >
			<p>
			<span class="zt-ls"><b>解</b></span>
			（3）
			先将精确度设置为0.01，再将科学计算器设置为弧度计算模式，然后依次按下列各键：
			</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0197-6.jpg" />
			</p>
			<p>结果显示：</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0197-7.jpg" />
			</p>
			<p>
			所以<math display="0">
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mfrac>
			<mrow>
			<mn>6</mn>
			<mi>π</mi>
			</mrow>
			<mn>5</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>≈</mo>
			<mo>−</mo>
			<mn>0.73</mn>
			<mo>.</mo>
			</math>
			</p>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[193]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
			</div>
			</div>
			</div>
			</div>
			<!-- 186 -->
			<div class="page-box" page="193">
			<div v-if="showPageList.indexOf(193) > -1">
			<ul class="page-header-odd fl al-end">
			<li>186</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			</div>
			<div class="page-box hidePage" page="193">
			</div>

			<!-- 187 -->
			<div class="page-box" page="194">
			<div v-if="showPageList.indexOf(194) > -1">
			@@ -462,7 +5371,13 @@
			<p><span>187</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<h3 id="c056">习题5.5<span class="fontsz2">＞＞＞</span></h3>
			<div class="bj">
			<examinations :cardList="questionData[194]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
			</div>
			</div>
			</div>
			</div>
			<!-- 188 -->
			@@ -473,10 +5388,64 @@
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<h2 id="b035">
			5.6 正弦函数的图像和性质<span class="fontsz1">＞＞＞＞＞＞＞＞</span>
			</h2>
			<h3 id="c057">
			5.6.1 正弦函数的图像<span class="fontsz2">＞＞＞</span>
			</h3>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/gcsk.jpg" />
			</p>
			<p>
			如果今天是2021年3月17日星期三，那么往前推7天是周几？往后推7天是周几？再过7天又是周几？
			</p>
			<p>显然，前面所有问题都是同一个答案：周三.</p>
			<p>
			生活中，像这样每隔7天，“周三”又会重复出现，这个“7天”就是我们常说的一周（一个周期），这种每隔一段时间便会重复出现的现象称为周期现象.
			</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0199-1.jpg" />
			</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>
			<p>
			我们知道，单位圆上任意一点在圆周上旋转一周就回到原来的位置，这说明，
			在函数<i>y</i>=sin<i>x</i>中，当自变量每间隔2π个单位长度时，对应的函数值都会重复出现，即sin（<i>x</i>+2π）=sin<i>x</i>.
			</p>
			<div class="bk">
			<div class="bj1">
			<p class="left">
			<img class="img-gn1" alt="" src="../../assets/images/gn.jpg" />
			</p>
			</div>
			<p class="block">周期函数</p>
			<p class="block">周期</p>
			<p class="block">最小正周期</p>
			</div>
			<p>
			一般地，对于函数<i>y</i>=<i>f</i>（<i>x</i>），如果存在一个非零常数<i>T</i>，当<i>x</i>取定义域<i>D</i>内的每一个值时，都有<i>x</i>+<i>T</i>∈<i>D</i>，并且都满足
			</p>
			<p class="center">
			<i>f</i>（<i>x</i>+<i>T</i>）=<i>f</i>（<i>x</i>），
			</p>
			<p>
			则称函数<i>y</i>=<i>f</i>（<i>x</i>）为<b>周期函数</b>，非零常数<i>T</i>叫作这个函数的一个<b>周期</b>.
			</p>
			<p>
			例如，函数<i>y</i>=sin<i>x</i>中，对于任意<i>x</i>∈<b>R</b>，都有<i>x</i>+2π∈<b>R</b>，且满足<i>f</i>（<i>x</i>+2π）=<i>f</i>（<i>x</i>）.可见，正弦函数是周期函数，且2π是它的一个周期.
			</p>
			<p>
			又由sin（<i>x</i>+2π<i>k</i>）=sin<i>x</i>（<i>k</i>∈<b>Z</b>），可知2π，4π，6π，…及-2π，-4π，-6π，…都是正弦函数<i>y</i>=sin<i>x</i>的周期.
			</p>
			<p>
			对于一个周期函数<i>y</i>=<i>f</i>（<i>x</i>），如果在它的所有的周期中存在一个最小的正数，就称这个最小的正数为<i>y</i>=<i>f</i>（<i>x</i>）的<b>最小正周期</b>.
			</p>
			</div>
			</div>
			</div>

			<!-- 189 -->
			<div class="page-box" page="196">
			<div v-if="showPageList.indexOf(196) > -1">
			@@ -488,10 +5457,90 @@
			<p><span>189</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p>
			由此可见，2π就是正弦函数<i>y</i>=sin<i>x</i>的最小正周期.为了简便起见，本书所指的三角函数的周期一般指函数的最小正周期.因此，我们说正弦函数的周期是2π.
			</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>
			<p>
			<i>y</i>=sin<i>x</i>是以2π为周期的函数，所以只要画出它在一个完整周期内的图像，再利用周期性就可以得到正弦函数的图像.
			</p>
			<p>
			首先，列表.自变量<i>x</i>的取值如表5-5所示，利用科学计算器求出<i>y</i>=sin<i>x</i>的各个值并填入表中.
			</p>
			<p class="img">表5-5</p>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0200-1.jpg" />
			</p>
			<p>
			其次，描点连线.根据表中数值描点，然后用光滑的曲线把各点连接起来，绘制出在［0，2π］上的图像，如图5-25所示.
			</p>
			<p class="center">
			<img class="img-b" alt="" src="../../assets/images/0200-2.jpg" />
			</p>
			<p class="img">图5-25</p>
			<p>
			由图5-25可以看出，决定函数<i>y</i>=sin<i>x</i>（<i>x</i>∈0，2π）
			图像形状的有五个关键点，即
			</p>
			<math display="block">
			<mo stretchy="false">(</mo>
			<mn>0</mn>
			<mo>,</mo>
			<mn>0</mn>
			<mo stretchy="false">)</mo>
			<mo>,</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo>,</mo>
			<mn>1</mn>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>,</mo>
			<mo stretchy="false">(</mo>
			<mi>π</mi>
			<mo>,</mo>
			<mn>0</mn>
			<mo stretchy="false">)</mo>
			<mo>,</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mrow>
			<mn>3</mn>
			<mi>π</mi>
			</mrow>
			<mn>2</mn>
			</mfrac>
			<mo>,</mo>
			<mo>−</mo>
			<mn>1</mn>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>,</mo>
			<mo stretchy="false">(</mo>
			<mn>2</mn>
			<mi>π</mi>
			<mo>,</mo>
			<mn>0</mn>
			<mo stretchy="false">)</mo>
			<mo>.</mo>
			</math>
			<p>
			因此，在精确度要求不高时，经常先找出这五个关键点，再用光滑的曲线将它们连接起来，得到函数<i>y</i>=sin<i>x</i>（<i>x</i>∈0，2π）的简图，我们称这种画图方法为“五点（画图）法”.
			</p>
			<p>
			最后，利用正弦函数的周期性，我们将函数<i>y</i>=sin<i>x</i>（<i>x</i>∈0，2π）的图像向左或向右平移2π，4π，…，即可画出<i>y</i>=sin<i>x</i>在<b>R</b>的图像，如图5-26所示.
			</p>
			</div>
			</div>
			</div>

			<!-- 190 -->
			<div class="page-box" page="197">
			<div v-if="showPageList.indexOf(197) > -1">
			@@ -500,10 +5549,73 @@
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="center">
			<img class="img-b" alt="" src="../../assets/images/0201-1.jpg" />
			</p>
			<p class="img">图5-26</p>
			<p>
			正弦函数<i>y</i>=sin<i>x</i>，<i>x</i>∈<b>R</b>的图像叫作正弦曲线.
			</p>
			<p>
			<span class="zt-ls"><b>例1</b></span>　用“五点法”画出下列函数在区间［0，2π］内的简图.
			</p>
			<p class="p-btn" >
			<span>
			（1） <i>y</i>=-sin<i>x</i>；
			</span>
			<span class="btn-box" @click="hadleAnswer(34)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer34" >
			<p>
			<span class="zt-ls"><b>解</b></span>（1）列表（表5-6）.
			</p>
			<p class="img">表5-6</p>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0201-2.jpg" />
			</p>
			<p>
			描点连线得<i>y</i>=-sin<i>x</i>在区间［0，2π］内的简图，如图5-27所示.
			</p>
			<p class="center">
			<img class="img-d" alt="" src="../../assets/images/0201-3.jpg" />
			</p>
			<p class="img">图5-27</p>
			</div>
			<p class="p-btn" >
			<span>（2） <i>y</i>=1+sin<i>x</i>.</span>
			<span class="btn-box" @click="hadleAnswer(35)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer35" >
			<p><span class="zt-ls"><b>解</b></span>（2）列表（表5-7）.</p>
			<p class="img">表5-7</p>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0201-4.jpg" />
			</p>
			<p>
			描点连线得<i>y</i>=1+sin<i>x</i>在区间［0，2π］内的简图，如图5-28所示.
			</p>
			<p class="center">
			<img class="img-d" alt="" src="../../assets/images/0201-5.jpg" />
			</p>
			<p class="img">图5-28</p>
			</div>
			<iframe src="https://www.geogebra.org/calculator" frameborder="0" class="iframe-box"></iframe>
			</div>
			</div>
			</div>

			<!-- 191 -->
			<div class="page-box" page="198">
			<div v-if="showPageList.indexOf(198) > -1">
			@@ -515,8 +5627,88 @@
			<p><span>191</span></p>
			</li>
			</ul>

			<div class="padding-116"></div>
			<div class="padding-116">
			<div class="bk-hzjl">
			<div class="bj1-hzjl">
			<p class="left">
			<img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
			</p>
			</div>
			<examinations :cardList="questionData[198]" :hideCollect="true" sourceType="json" v-if="questionData">
			</examinations>
			<p class="block">
			<i>y</i>=-sin<i>x</i>与<i>y</i>=sin<i>x</i>的图像有什么关系？
			<i>y</i>=1+sin<i>x</i>与<i>y</i>=sin<i>x</i>的图像有什么关系？
			</p>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<fillInTable :queryData="queryDataOne" />
			<paint
			:page="198"
			:imgUrl="this.config.activeBook.resourceUrl + '/images/0103-2.jpg'"
			/>
			</div>
			<h3 id="c058">
			5.6.2 正弦函数的性质（一）<span class="fontsz2">＞＞＞</span>
			</h3>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
			</p>
			<p>
			通过观察<i>y</i>=sin<i>x</i>的图像可知正弦函数<i>y</i>=sin<i>x</i>的性质.本节主要研究正弦函数的定义域、值域、周期性和奇偶性.
			</p>
			<p>1.定义域.</p>
			<p><i>y</i>=sin<i>x</i>的定义域是<b>R</b>.</p>
			<p>2.值域.</p>
			<p>
			曲线夹在两条直线<i>y</i>=1和<i>y</i>=-1之间，因此-1≤sin<i>x</i>≤1，即<i>y</i>=sin<i>x</i>的值域是［-1，1］.
			</p>
			<p>
			当<math display="0">
			<mi>x</mi>
			<mo>=</mo>
			<mn>2</mn>
			<mi>k</mi>
			<mi>π</mi>
			<mo>+</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo stretchy="false">(</mo>
			<mi>k</mi>
			<mo>∈</mo>
			<mrow>
			<mi mathvariant="bold">Z</mi>
			</mrow>
			<mo stretchy="false">)</mo>
			</math>时，<i>y</i>=sin <i>x</i>取得最大值1；
			</p>
			<p>
			当<math display="0">
			<mi>x</mi>
			<mo>=</mo>
			<mn>2</mn>
			<mi>k</mi>
			<mi>π</mi>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo stretchy="false">(</mo>
			<mi>k</mi>
			<mo>∈</mo>
			<mrow>
			<mi mathvariant="bold">Z</mi>
			</mrow>
			<mo stretchy="false">)</mo>
			</math>时，<i>y</i>=sin <i>x</i>取得最小值-1.
			</p>
			</div>
			</div>
			</div>

			@@ -524,29 +5716,565 @@
			<div class="page-box" page="199">
			<div v-if="showPageList.indexOf(199) > -1">
			<ul class="page-header-odd fl al-end">
			<li>192</li>
			<li>192-193</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>

			<div class="padding-116"></div>
			<div class="padding-116">
			<p>3.周期性.</p>
			<p><i>y</i>=sin<i>x</i>是周期函数，周期是2π.</p>
			<p>4.奇偶性.</p>
			<p>
			因为sin（-<i>x</i>）=-sin<i>x</i>，所以<i>y</i>=sin<i>x</i>是奇函数，其图像关于原点对称.
			</p>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例1</b></span>　已知<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mn>3</mn>
			<mo>−</mo>
			<mi>a</mi>
			</mrow>
			<mn>2</mn>
			</mfrac>
			</math>，求<i>a</i>的取值范围.
			</span>
			<span class="btn-box" @click="hadleAnswer(36)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer36" >
			<p>
			<span class="zt-ls"><b>解</b></span> 因为　-1≤sin<i>x</i>≤1，
			</p>
			<p>
			所以　<math display="0">
			<mo>−</mo>
			<mn>1</mn>
			<mo>⩽</mo>
			<mfrac>
			<mrow>
			<mn>3</mn>
			<mo>−</mo>
			<mi>a</mi>
			</mrow>
			<mn>2</mn>
			</mfrac>
			<mo>⩽</mo>
			<mn>1</mn>
			</math>，
			</p>
			<p>解得　1≤<i>a</i>≤5.</p>
			</div>
			<p>
			<span class="zt-ls"><b>例2</b></span>　求使下列函数取得最大值、最小值的<i>x</i>的集合，并求出这些函数的最大值、最小值.
			</p>
			<p class="p-btn" >
			<span>
			（1） <i>y</i>=3+sin<i>x</i>；
			</span>
			<span class="btn-box" @click="hadleAnswer(37)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer37" >
			<p>
			<span class="zt-ls"><b>解</b></span>（1）
			使函数<i>y</i>=3+sin<i>x</i>取得最大值的<i>x</i>的集合，就是使函数<i>y</i>=sin<i>x</i>取得最大值的<i>x</i>的集合<math display="0">
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">{</mo>
			<mi>x</mi>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">\|</mo>
			<mstyle scriptlevel="0">
			<mspace width="thinmathspace"></mspace>
			</mstyle>
			<mi>x</mi>
			<mo>=</mo>
			<mn>2</mn>
			<mi>k</mi>
			<mi>π</mi>
			<mo>+</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
			</mrow>
			<mo>,</mo>
			<mi>k</mi>
			<mo>∈</mo>
			<mrow>
			<mi mathvariant="bold">Z</mi>
			</mrow>
			<mo data-mjx-texclass="CLOSE">}</mo>
			</mrow>
			</math>.这时函数<i>y</i>=3+sin<i>x</i>的最大值为<i>y</i>=3+1=4.
			</p>
			<p>
			使函数<i>y</i>=3+sin<i>x</i>取得最小值的<i>x</i>的集合，就是使函数<i>y</i>=sin<i>x</i>取得最小值的<i>x</i>的集合<math display="0">
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">{</mo>
			<mi>x</mi>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">\|</mo>
			<mstyle scriptlevel="0">
			<mspace width="thinmathspace"></mspace>
			</mstyle>
			<mi>x</mi>
			<mo>=</mo>
			<mn>2</mn>
			<mi>k</mi>
			<mi>π</mi>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
			</mrow>
			<mo>,</mo>
			<mi>k</mi>
			<mo>∈</mo>
			<mrow>
			<mi mathvariant="bold">Z</mi>
			</mrow>
			<mo data-mjx-texclass="CLOSE">}</mo>
			</mrow>
			</math>.这时函数<i>y</i>=3+sin<i>x</i>的最小值为<i>y</i>=3+（-1）=2.
			</p>
			</div>
			<p class="p-btn" >
			<span>
			（2） <i>y</i>=-2sin<i>x</i>.
			</span>
			<span class="btn-box" @click="hadleAnswer(38)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer38" >
			<p>
			<span class="zt-ls"><b>解</b></span>（2）
			使函数<i>y</i>=-2sin<i>x</i>取得最大值的<i>x</i>的集合，就是使函数<i>y</i>=sin<i>x</i>取得最小值的<i>x</i>的集合<math display="0">
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">{</mo>
			<mi>x</mi>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">\|</mo>
			<mstyle scriptlevel="0">
			<mspace width="thinmathspace"></mspace>
			</mstyle>
			<mi>x</mi>
			<mo>=</mo>
			<mn>2</mn>
			<mi>k</mi>
			<mi>π</mi>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
			</mrow>
			<mo>,</mo>
			<mi>k</mi>
			<mo>∈</mo>
			<mrow>
			<mi mathvariant="bold">Z</mi>
			</mrow>
			<mo data-mjx-texclass="CLOSE">}</mo>
			</mrow>
			</math>.这时函数<i>y</i>=-2sin<i>x</i>的最大值为<i>y</i>=-2×（-1）=2.
			</p>
			<p>
			使函数<i>y</i>=-2sin<i>x</i>取得最小值的<i>x</i>的集合，就是使函数<i>y</i>=sin<i>x</i>取得最大值的<i>x</i>的集合<math display="0">
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">{</mo>
			<mi>x</mi>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">\|</mo>
			<mstyle scriptlevel="0">
			<mspace width="thinmathspace"></mspace>
			</mstyle>
			<mi>x</mi>
			<mo>=</mo>
			<mn>2</mn>
			<mi>k</mi>
			<mi>π</mi>
			<mo>+</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
			</mrow>
			<mo>,</mo>
			<mi>k</mi>
			<mo>∈</mo>
			<mrow>
			<mi mathvariant="bold">Z</mi>
			</mrow>
			<mo data-mjx-texclass="CLOSE">}</mo>
			</mrow>
			</math>.这时函数<i>y</i>=-2sin<i>x</i>的最小值为<i>y</i>=-2×1=-2.
			</p>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[199]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
			</div>
			<h3 id="c059">
			5.6.3 正弦函数的性质（二）<span class="fontsz2">＞＞＞</span>
			</h3>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>
			<p>5.单调性.</p>
			<p>
			如图5-29所示，选取正弦曲线在长度为2π的区间<math display="0">
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">[</mo>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo>,</mo>
			<mfrac>
			<mrow>
			<mn>3</mn>
			<mi>π</mi>
			</mrow>
			<mn>2</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">]</mo>
			</mrow>
			</math>内的图像进行考查.
			</p>
			<p class="center">
			<img class="img-d" alt="" src="../../assets/images/0204-3.jpg" />
			</p>
			<p class="img">图5-29</p>
			<p>
			<i>y</i>=sin<i>x</i> 在区间<math display="0">
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">[</mo>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo>,</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">]</mo>
			</mrow>
			</math>上是增函数，在区间<math display="0">
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">[</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo>,</mo>
			<mfrac>
			<mrow>
			<mn>3</mn>
			<mi>π</mi>
			</mrow>
			<mn>2</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">]</mo>
			</mrow>
			</math>上是减函数.由正弦函数的周期性可知：<i>y</i>=sin<i>x</i>在每一个区间<math display="0">
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">[</mo>
			<mn>2</mn>
			<mi>k</mi>
			<mi>π</mi>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo>,</mo>
			<mn>2</mn>
			<mi>k</mi>
			<mi>π</mi>
			<mo>+</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">]</mo>
			</mrow>
			</math>上都是增函数，函数值由-1增大到1；在每一个区间<math display="0">
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">[</mo>
			<mn>2</mn>
			<mi>k</mi>
			<mi>π</mi>
			<mo>+</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo>,</mo>
			<mn>2</mn>
			<mi>k</mi>
			<mi>π</mi>
			<mo>+</mo>
			<mfrac>
			<mrow>
			<mn>3</mn>
			<mi>π</mi>
			</mrow>
			<mn>2</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">]</mo>
			</mrow>
			</math>上都是减函数，函数值由1减小到-1.
			</p>
			<p>
			<b>例</b> 不求值，利用正弦函数的单调性，比较下列各对正弦值的大小.
			</p>
			<p class="p-btn" >
			<span>
			（1）<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>3</mn>
			<mi>π</mi>
			</mrow>
			<mn>4</mn>
			</mfrac>
			</math>与<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>2</mn>
			<mi>π</mi>
			</mrow>
			<mn>3</mn>
			</mfrac>
			</math>；
			</span>
			<span class="btn-box" @click="hadleAnswer(39)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer39" >
			<p>
			<span class="zt-ls"><b>解</b></span>（1）因为　<math display="0">
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo><</mo>
			<mfrac>
			<mrow>
			<mn>2</mn>
			<mi>π</mi>
			</mrow>
			<mn>3</mn>
			</mfrac>
			<mo><</mo>
			<mfrac>
			<mrow>
			<mn>3</mn>
			<mi>π</mi>
			</mrow>
			<mn>4</mn>
			</mfrac>
			<mo><</mo>
			<mfrac>
			<mrow>
			<mn>3</mn>
			<mi>π</mi>
			</mrow>
			<mn>2</mn>
			</mfrac>
			</math>，
			</p>
			<p>
			而<i>y</i>=sin <i>x</i> 在<math display="0">
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">[</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo>,</mo>
			<mfrac>
			<mrow>
			<mn>3</mn>
			<mi>π</mi>
			</mrow>
			<mn>2</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">]</mo>
			</mrow>
			</math>上是减函数，所以
			</p>
			<math display="block">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>3</mn>
			<mi>π</mi>
			</mrow>
			<mn>4</mn>
			</mfrac>
			<mo><</mo>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>2</mn>
			<mi>π</mi>
			</mrow>
			<mn>3</mn>
			</mfrac>
			<mtext>. </mtext>
			</math>
			</div>
			<p class="p-btn" >
			<span>
			（2）<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>9</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>与<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>10</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>.
			</span>
			<span class="btn-box" @click="hadleAnswer(40)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer40" >
			<p>
			<span class="zt-ls"><b>解</b></span>（2）因为　<math display="0">
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo><</mo>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>9</mn>
			</mfrac>
			<mo><</mo>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>10</mn>
			</mfrac>
			<mo><</mo>
			<mn>0</mn>
			</math>，
			</p>
			<p>
			而<i>y</i>=sin <i>x</i>在<math display="0">
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">[</mo>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo>,</mo>
			<mn>0</mn>
			<mo data-mjx-texclass="CLOSE">]</mo>
			</mrow>
			</math>上是增函数，所以
			</p>
			<math display="block">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>9</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo><</mo>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>10</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>
			</div>
			</div>
			</div>
			</div>

			<!-- 193 -->
			<div class="page-box" page="200">
			<div v-if="showPageList.indexOf(200) > -1">
			<ul class="page-header-box">
			<li>
			<p>第五单元三角函数</p>
			</li>
			<li>
			<p><span>193</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			</div>
			</div>
			<div class="page-box hidePage" page="200"></div>

			<!-- 194 -->
			<div class="page-box" page="201">
			@@ -556,10 +6284,22 @@
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[201] ? questionData[201][1] : []" :hideCollect="true"
			sourceType="json" inputBc="#d3edfa" v-if="questionData"></examinations>
			</div>
			<h3 id="c060">习题5.6<span class="fontsz2">＞＞＞</span></h3>
			<div class="bj">
			<examinations :cardList="questionData[201] ? questionData[201][2] : []" :hideCollect="true"
			sourceType="json" inputBc="#d3edfa" v-if="questionData"></examinations>
			</div>
			</div>
			</div>
			</div>

			<!-- 195 -->
			<div class="page-box" page="202">
			<div v-if="showPageList.indexOf(202) > -1">
			@@ -571,7 +6311,51 @@
			<p><span>195</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<h2 id="b036">
			5.7 余弦函数的图像和性质<span class="fontsz1">＞＞＞＞＞＞＞＞</span>
			</h2>
			<h3 id="c061">
			5.7.1 余弦函数的图像<span class="fontsz2">＞＞＞</span>
			</h3>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/wttc.jpg" />
			</p>
			<p>
			我们学习了正弦函数的图像和性质，你能用类似的方法绘制出余弦函数的图像，并根据图像研究它的性质吗？
			</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>
			<p>根据诱导公式可知，</p>
			<p class="center">cos（<i>x</i>+2π）=cos <i>x</i>.</p>
			<p>
			由周期函数的定义可知，余弦函数<i>y</i>=cos<i>x</i>是以2π为周期的周期函数.为画出函数<i>y</i>=cos<i>x</i>的图像，可仿照正弦曲线的画法，先用描点法画出它在一个周期［0，2π］内的图像，然后利用周期性画出其完整图像.
			</p>
			<p>
			首先，列表.自变量<i>x</i>取值如表5-9所示，利用科学计算器求出cos
			<i>x</i>的各个值并填入表中.
			</p>
			<p class="img">表5-9</p>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0206-1.jpg" />
			</p>
			<p>
			其次，描点连线.根据表中数值描点，用光滑的曲线把各点连接起来，得出图像如图5-30所示.
			</p>
			<p class="center">
			<img class="img-d" alt="" src="../../assets/images/0206-2.jpg" />
			</p>
			<p class="img">图5-30</p>
			<p>
			最后，利用余弦函数的周期性，把<i>y</i>=cos
			<i>x</i>在［0，2π］内的图像向左或向右平移2π，4π，…就可以画出<i>y</i>=cos
			<i>x</i>在<b>R</b>上的图像，如图5-31所示.
			</p>
			<p>
			余弦函数<i>y</i>=cos<i>x</i>，<i>x</i>∈<b>R</b>的图像叫作<b>余弦曲线</b>.
			</p>
			</div>
			</div>
			</div>
			<!-- 196 -->
			@@ -582,10 +6366,135 @@
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="center">
			<img class="img-b" alt="" src="../../assets/images/0207-1.jpg" />
			</p>
			<p class="img">图5-31</p>
			<div class="bk">
			<div class="bj1">
			<p class="left">
			<img class="img-gn1" alt="" src="../../assets/images/tbts.jpg" />
			</p>
			</div>
			<p class="block">
			1.与画正弦函数的图像一样，也可以用“五点法”画出<i>y</i>=cos<i>x</i>在0，2π内的简图，这五个关键点是：
			</p>
			<math display="block">
			<mo stretchy="false">(</mo>
			<mn>0</mn>
			<mo>,</mo>
			<mn>1</mn>
			<mo stretchy="false">)</mo>
			<mo>,</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo>,</mo>
			<mn>0</mn>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>,</mo>
			<mo stretchy="false">(</mo>
			<mi>π</mi>
			<mo>,</mo>
			<mo>−</mo>
			<mn>1</mn>
			<mo stretchy="false">)</mo>
			<mo>,</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mfrac>
			<mrow>
			<mn>3</mn>
			<mi>π</mi>
			</mrow>
			<mn>2</mn>
			</mfrac>
			<mo>,</mo>
			<mn>0</mn>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>,</mo>
			<mo stretchy="false">(</mo>
			<mn>2</mn>
			<mi>π</mi>
			<mo>,</mo>
			<mn>1</mn>
			<mo stretchy="false">)</mo>
			<mtext>. </mtext>
			</math>
			<p class="block">
			2.正弦函数的图像向左平移<math display="0">
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			</math>个单位长度即可得到余弦函数的图像，如图5-32所示.
			</p>
			<p class="center">
			<img class="img-b" alt="" src="../../assets/images/0207-4.jpg" />
			</p>
			<p class="img">图5-32</p>
			</div>
			<p><b>例</b> 用“五点法”画出下列函数在区间［0，2π］内的简图.</p>
			<p class="p-btn" >
			<span>（1） <i>y</i>=2cos <i>x</i>；</span>
			<span class="btn-box" @click="hadleAnswer(41)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p class="p-btn" >
			<span>（2） <i>y</i>=-1+cos <i>x</i>.</span>
			<span class="btn-box" @click="hadleAnswer(42)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<iframe src="https://www.geogebra.org/calculator" frameborder="0" class="iframe-box"></iframe>
			<div v-if="isShowAnswer41" >
			<p>
			<span class="zt-ls"><b>解</b></span>（1）列表（表5-10）.
			</p>
			<p class="img">表5-10</p>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0207-5.jpg" />
			</p>
			<p class="center">
			<img class="img-f" alt="" src="../../assets/images/0207-6.jpg" />
			</p>
			<p class="img">图5-33</p>
			<p>描点连线得<i>y</i>=2cos <i>x</i>在区间［0，2π］</p>
			<p>内的简图，如图5-33所示.</p>
			</div>
			<div v-if="isShowAnswer42" >
			<p>（2）列表（表5-11）.</p>
			<p class="img">表5-11</p>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0208-1.jpg" />
			</p>
			<p>
			描点连线得<i>y</i>=-1+cos
			<i>x</i>在区间［0，2π］内的简图，如图5-34所示.
			</p>
			<p class="center">
			<img class="img-d" alt="" src="../../assets/images/0208-2.jpg" />
			</p>
			<p class="img">图5-34</p>
			</div>
			</div>
			</div>
			</div>

			<!-- 197 -->
			<div class="page-box" page="204">
			<div v-if="showPageList.indexOf(204) > -1">
			@@ -597,10 +6506,38 @@
			<p><span>197</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">

			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<fillInTable :queryData="queryDataTwo" />
			<p>
			对比<i>y</i>=cos <i>x</i>的图像，<i>y</i>=1-cos
			<i>x</i>图像是将<i>y</i>=cos <i>x</i>的图像通过
			<input type="text" class="input-table" />
			变化而得到的.
			<span class="btn-box" @click="isShowAnswer = !isShowAnswer" >
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p class="table-answer-box" v-if="isShowAnswer">
			答案：翻转和平移
			</p>
			<paint
			:page="204"
			:canvasHeight="200"
			:imgUrl="this.config.activeBook.resourceUrl + '/images/0208-4.jpg'"
			/>
			</div>
			</div>
			</div>
			</div>

			<!-- 198 -->
			<div class="page-box" page="205">
			<div v-if="showPageList.indexOf(205) > -1">
			@@ -609,7 +6546,74 @@
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<h3 id="c062">
			5.7.2 余弦函数的性质<span class="fontsz2">＞＞＞</span>
			</h3>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
			</p>
			<p>
			通过观察<i>y</i>=cos <i>x</i>的图像可知，余弦函数<i>y</i>=cos
			<i>x</i>的性质有：
			</p>
			<p>1.定义域.</p>
			<p><i>y</i>=cos <i>x</i>的定义域是<b>R</b>.</p>
			<p>2.值域.</p>
			<p>
			由余弦函数的图像可以看出，曲线夹在两条直线<i>y</i>=1和<i>y</i>=-1之间，因此-1≤cos
			<i>x</i>≤1，即<i>y</i>=cos <i>x</i>的值域是［-1，1］.
			</p>
			<p>
			当<i>x</i>=2<i>k</i>π（<i>k</i>∈<b>Z</b>）时，<i>y</i>=cos
			<i>x</i>取得最大值1；
			</p>
			<p>
			当<i>x</i>=2<i>k</i>π+π（<i>k</i>∈<b>Z</b>）时，<i>y</i>=cos
			<i>x</i>取得最小值-1.
			</p>
			<p>3.周期性.</p>
			<p><i>y</i>=cos <i>x</i>是周期函数，周期是2π.</p>
			<p>4.奇偶性.</p>
			<p>
			因为cos（-<i>x</i>）=cos <i>x</i>，所以<i>y</i>=cos
			<i>x</i>是偶函数，其图像关于<i>y</i>轴对称.
			</p>
			<p>5.单调性.</p>
			<p>
			<i>y</i>=cos
			<i>x</i>在区间［0，π］上是减函数，在［π，2π］上是增函数.
			</p>
			<p>
			余弦函数<i>y</i>=cos
			<i>x</i>在每一个区间［2<i>k</i>π，2<i>k</i>π+π］（<i>k</i>∈<b>Z</b>）上都是减函数，其值由1减小到-1；在每一个区间［2<i>k</i>π+π，2<i>k</i>π+2π］（<i>k</i>∈<b>Z</b>）上都是增函数，其值由-1增大到1.
			</p>
			<p class="p-btn" >
			<span><span class="zt-ls"><b>例1</b></span>　求函数<i>y</i>=-1+cos <i>x</i>的最大值、最小值、最小正周期及值域.</span>
			<span class="btn-box" @click="hadleAnswer(43)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer43" >
			<p>
			<span class="zt-ls"><b>解</b></span>
			当<i>x</i>=2<i>k</i>π（<i>k</i>∈<b>Z</b>）时，函数<i>y</i>=-1+cos
			<i>x</i>的最大值为<i>y</i>=1-1=0；
			</p>
			<p>
			当<i>x</i>=2<i>k</i>π+π（<i>k</i>∈<i>Z</i>）时，函数<i>y</i>=-1+cos
			<i>x</i>的最小值为<i>y</i>=-1-1=-2；
			</p>
			<p>
			函数<i>y</i>=-1+cos <i>x</i>的最小正周期为2π；函数<i>y</i>=-1+cos
			<i>x</i>的值域为[-2，0].
			</p>
			</div>
			</div>
			</div>
			</div>
			<!-- 199 -->
			@@ -623,11 +6627,280 @@
			<p><span>199</span></p>
			</li>
			</ul>

			<div class="padding-116"></div>
			<div class="padding-116">
			<div class="bk-hzjl">
			<div class="bj1-hzjl">
			<p class="left">
			<img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
			</p>
			</div>
			<examinations :cardList="questionData[206] ? questionData[206][1] : []" :hideCollect="true"
			sourceType="json" v-if="questionData"></examinations>
			</div>
			<p>
			<span class="zt-ls"><b>例2</b></span>　不求值，利用余弦函数的单调性，比较下列各对余弦值的大小.
			</p>
			<p class="p-btn" >
			<span>
			（1）
			<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>6</mn>
			<mi>π</mi>
			</mrow>
			<mn>5</mn>
			</mfrac>
			</math>与<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>5</mn>
			<mi>π</mi>
			</mrow>
			<mn>4</mn>
			</mfrac>
			</math>；
			</span>
			<span class="btn-box" @click="hadleAnswer(44)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer44" >
			<p>
			<span class="zt-ls"><b>解</b></span>（1）因为<math display="0">
			<mi>π</mi>
			<mo><</mo>
			<mfrac>
			<mrow>
			<mn>6</mn>
			<mi>π</mi>
			</mrow>
			<mn>5</mn>
			</mfrac>
			<mo><</mo>
			<mfrac>
			<mrow>
			<mn>5</mn>
			<mi>π</mi>
			</mrow>
			<mn>4</mn>
			</mfrac>
			<mo><</mo>
			<mfrac>
			<mrow>
			<mn>3</mn>
			<mi>π</mi>
			</mrow>
			<mn>2</mn>
			</mfrac>
			</math>，而函数<i>y</i>=cos <i>x</i>在<math display="0">
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">[</mo>
			<mi>π</mi>
			<mo>,</mo>
			<mfrac>
			<mrow>
			<mn>3</mn>
			<mi>π</mi>
			</mrow>
			<mn>2</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">]</mo>
			</mrow>
			</math>上是增函数，所以
			</p>
			<math display="block">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>6</mn>
			<mi>π</mi>
			</mrow>
			<mn>5</mn>
			</mfrac>
			<mo><</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>5</mn>
			<mi>π</mi>
			</mrow>
			<mn>4</mn>
			</mfrac>
			<mo>.</mo>
			</math>
			</div>
			<p class="p-btn" >
			<span>
			（2）
			<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>7</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>与<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>8</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>.
			</span>
			<span class="btn-box" @click="hadleAnswer(45)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer45" >
			<p>
			<span class="zt-ls"><b>解</b></span>（2）<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>7</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>7</mn>
			</mfrac>
			</math>，<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>8</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>8</mn>
			</mfrac>
			</math>.
			</p>
			<p>
			因为<math display="0">
			<mn>0</mn>
			<mo><</mo>
			<mfrac>
			<mi>π</mi>
			<mn>8</mn>
			</mfrac>
			<mo><</mo>
			<mfrac>
			<mi>π</mi>
			<mn>7</mn>
			</mfrac>
			<mo><</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			</math>，而函数<i>y</i>=cos <i>x</i>在0，<math display="0">
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">[</mo>
			<mn>0</mn>
			<mo>,</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">]</mo>
			</mrow>
			</math>上是减函数，所以<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>7</mn>
			</mfrac>
			<mo><</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>8</mn>
			</mfrac>
			</math>，即
			</p>
			<math display="block">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>7</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo><</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>8</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>.</mo>
			</math>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[206] ? questionData[206][2] : []" :hideCollect="true"
			sourceType="json" inputBc="#d3edfa" v-if="questionData"></examinations>
			</div>
			</div>
			</div>
			</div>

			<!-- 200 -->
			<div class="page-box" page="207">
			<div v-if="showPageList.indexOf(207) > -1">
			@@ -636,7 +6909,57 @@
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<h3 id="c063">习题5.7<span class="fontsz2">＞＞＞</span></h3>
			<div class="bj">
			<examinations :cardList="questionData[207]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
			</div>
			<h2 id="b037">
			5.8 已知三角函数值，求指定范围的角<span class="fontsz1">＞＞＞＞＞＞＞＞</span>
			</h2>
			<h3 id="c064">
			5.8.1 已知特殊三角函数值求角<span class="fontsz2">＞＞＞</span>
			</h3>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/wttc.jpg" />
			</p>
			<p>
			如果<math display="0">
			<mi>x</mi>
			<mo>=</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			</math>，那么<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</math>；反之，如果<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</math>，那么<math display="0">
			<mi>x</mi>
			<mo>=</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			</math>吗？
			</p>
			</div>
			</div>
			</div>
			<!-- 201 -->
			@@ -650,10 +6973,262 @@
			<p><span>201</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>
			<p>
			由<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</math>可知，<math display="0">
			<mi>x</mi>
			<mo>=</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			</math>是满足<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</math>的一个角，还有没有更多的角也能满足<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</math>呢？我们借助正弦曲线来探究问题.
			</p>
			<p>
			如图5-35所示，条件中的<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</math>，在图像中就可以表示为<math display="0">
			<mi>y</mi>
			<mo>=</mo>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</math>，问题就转化为求当<math display="0">
			<mi>y</mi>
			<mo>=</mo>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</math>的值，即直线<math display="0">
			<mi>y</mi>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</math>与正弦曲线<i>y</i>=sin <i>x</i>交点所对应的<i>x</i>的值.
			</p>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0212-9.jpg" />
			</p>
			<p class="img">图5-35</p>
			<p>
			观察图像可知，直线<math display="0">
			<mi>y</mi>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</math>与正弦曲线<i>y</i>=sin <i>x</i>的交点有无数个.
			</p>
			<p>
			现将问题的范围限定为<i>x</i>∈［0，2π］，由图像可知，满足条件的交点共有两个.
			</p>
			<p>
			因为<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			<mo>＞</mo>
			<mn>0</mn>
			</math>，所以<i>x</i>是第一或第二象限角.
			</p>
			<p>
			满足<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</math>的锐角是<math display="0">
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			</math>，所以符合条件的第一象限的角是<math display="0">
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			</math>.
			</p>
			<p>
			由诱导公式<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mi>π</mi>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</math>可知，<math display="0">
			<mi>x</mi>
			<mo>=</mo>
			<mi>π</mi>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mn>5</mn>
			<mi>π</mi>
			</mrow>
			<mn>6</mn>
			</mfrac>
			</math>，所以符合条件的第二象限角是<math display="0">
			<mfrac>
			<mrow>
			<mn>5</mn>
			<mi>π</mi>
			</mrow>
			<mn>6</mn>
			</mfrac>
			</math>.
			</p>
			<p>
			所以
			<math display="0">
			<mi>x</mi>
			<mo>=</mo>
			<mfrac>
			<mi>π</mi>
			<mn>6</mn>
			</mfrac>
			</math>或<math display="0">
			<mi>x</mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mn>5</mn>
			<mi>π</mi>
			</mrow>
			<mn>6</mn>
			</mfrac>
			</math>.
			</p>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例1</b></span>　已知<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			<mo>=</mo>
			<mo>−</mo>
			<mfrac>
			<msqrt>
			<mn>2</mn>
			</msqrt>
			<mn>2</mn>
			</mfrac>
			</math>，且<i>x</i>∈［0，2π］，求<i>x</i>的值.
			</span>
			<span class="btn-box" @click="hadleAnswer(46)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<p v-if="isShowAnswer46">
			<span class="zt-ls"><b>解</b></span> 因为<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			<mo>=</mo>
			<mo>−</mo>
			<mfrac>
			<msqrt>
			<mn>2</mn>
			</msqrt>
			<mn>2</mn>
			</mfrac>
			<mo>＜</mo>
			<mn>0</mn>
			</math>，所以<i>x</i>是第二或第三象限角.
			</p>
			</div>
			</div>
			</div>

			<!-- 202 -->
			<div class="page-box" page="209">
			<div v-if="showPageList.indexOf(209) > -1">
			@@ -662,10 +7237,336 @@
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p>
			满足<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<msqrt>
			<mn>2</mn>
			</msqrt>
			<mn>2</mn>
			</mfrac>
			</math>的锐角是<math display="0">
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mi>π</mi>
			<mn>4</mn>
			</mfrac>
			</math>，所以
			</p>
			<p>
			符合条件的第二象限角是<math display="0">
			<mi>x</mi>
			<mo>=</mo>
			<mi>π</mi>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>4</mn>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mn>3</mn>
			<mi>π</mi>
			</mrow>
			<mn>4</mn>
			</mfrac>
			</math>；
			</p>
			<p>
			符合条件的第三象限角是<math display="0">
			<mi>x</mi>
			<mo>=</mo>
			<mi>π</mi>
			<mo>+</mo>
			<mfrac>
			<mi>π</mi>
			<mn>4</mn>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mn>5</mn>
			<mi>π</mi>
			</mrow>
			<mn>4</mn>
			</mfrac>
			</math>.
			</p>
			<p>
			所以<math display="0">
			<mi>x</mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mn>3</mn>
			<mi>π</mi>
			</mrow>
			<mn>4</mn>
			</mfrac>
			</math>或<math display="0">
			<mi>x</mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mn>5</mn>
			<mi>π</mi>
			</mrow>
			<mn>4</mn>
			</mfrac>
			</math>.
			</p>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例2</b></span>　已知<math display="0">
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			<mo>=</mo>
			<msqrt>
			<mn>3</mn>
			</msqrt>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mi>x</mi>
			<mo>≠</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo>+</mo>
			<mi>k</mi>
			<mi>π</mi>
			<mo>,</mo>
			<mi>k</mi>
			<mo>∈</mo>
			<mrow>
			<mi mathvariant="bold">Z</mi>
			</mrow>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>，且0°≤<i>x</i>≤360°，求<i>x</i>的值.
			</span>
			<span class="btn-box" @click="hadleAnswer(47)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer47" >
			<p>
			<span class="zt-ls"><b>解</b></span> 因为<math display="0">
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			<mo>=</mo>
			<msqrt>
			<mn>3</mn>
			</msqrt>
			<mo>＞</mo>
			<mn>0</mn>
			</math>，所以<i>x</i>是第一或第三象限角.
			</p>
			<p>
			由<math display="0">
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mn>60</mn>
			<mrow>
			<mo>°</mo>
			</mrow>
			<mo>=</mo>
			<msqrt>
			<mn>3</mn>
			</msqrt>
			</math>可知，符合条件的第一象限角是<i>x</i>=60°.
			</p>
			<p>
			又因为<math display="0">
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mn>180</mn>
			<mrow>
			<mo>°</mo>
			</mrow>
			<mo>+</mo>
			<mn>60</mn>
			<mrow>
			<mo>°</mo>
			</mrow>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mn>60</mn>
			<mrow>
			<mo>°</mo>
			</mrow>
			<mo>=</mo>
			<msqrt>
			<mn>3</mn>
			</msqrt>
			</math>，
			</p>
			<p>所以符合条件的第三象限角是<i>x</i>=180°+60°=240°.</p>
			<p>所以<i>x</i>=60°或<i>x</i>=240°.</p>
			</div>
			<div class="bk">
			<div class="bj1">
			<p class="left">
			<img class="img-gn1" alt="" src="../../assets/images/tbts.jpg" />
			</p>
			</div>
			<p class="block">
			已知三角函数值，求给定范围的角<i>x</i>的值，其基本步骤如下.
			</p>
			<p class="block">
			（1）根据已知三角函数值的符号，判定角<i>x</i>所在的象限；
			</p>
			<p class="block">（2）求出满足三角函数值的锐角<i>x</i>′；</p>
			<p class="block">
			（3）
			根据<i>x</i>所在的象限和诱导公式，写出满足题目给定范围的<i>x</i>的值.
			</p>
			</div>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例3</b></span>　已知<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</math>，且<i>x</i>∈［-π，π］，求<i>x</i>的值.
			</span>
			<span class="btn-box" @click="hadleAnswer(48)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer48" >
			<p>
			<span class="zt-ls"><b>解</b></span> 因为<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			<mo>＞</mo>
			<mn>0</mn>
			</math>，所以<i>x</i>是第一或第四象限角.
			</p>
			<p>
			满足<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>x</mi>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</math>的锐角是<math display="0">
			<mi>x</mi>
			<mo>=</mo>
			<mfrac>
			<mi>π</mi>
			<mn>3</mn>
			</mfrac>
			</math>，所以符合条件的第一象限角是<math display="0">
			<mfrac>
			<mi>π</mi>
			<mn>3</mn>
			</mfrac>
			</math>.
			</p>
			<p>
			因为<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>3</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>3</mn>
			</mfrac>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			</math>，
			</p>
			<p>
			所以符合条件的第四象限角是<math display="0">
			<mi>x</mi>
			<mo>=</mo>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>3</mn>
			</mfrac>
			</math>.
			</p>
			<p>
			所以<math display="0">
			<mi>x</mi>
			<mo>=</mo>
			<mfrac>
			<mi>π</mi>
			<mn>3</mn>
			</mfrac>
			</math>或<math display="0">
			<mi>x</mi>
			<mo>=</mo>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>3</mn>
			</mfrac>
			</math>.
			</p>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[209]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
			</div>
			</div>
			</div>
			</div>

			<!-- 203 -->
			<div class="page-box" page="210">
			<div v-if="showPageList.indexOf(210) > -1">
			@@ -677,7 +7578,124 @@
			<p><span>203</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<h3 id="c065">
			5.8.2 已知任意三角函数值求角<span class="fontsz2">＞＞＞</span>
			</h3>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/wttc.jpg" />
			</p>
			<p>
			我们已经探究了已知特殊的三角函数值求角的方法，而对于不是特殊的三角函数值，又该如何求角呢？
			</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>
			<p>
			根据已知特殊的三角函数值求角的方法，借助计算工具，可以解决已知任意三角函数值求角的问题.
			</p>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例1</b></span>　已知<math display="0">
			<mi>α</mi>
			<mo>∈</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">[</mo>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo>,</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">]</mo>
			</mrow>
			</math>，求<i>α</i>的值.（结果精确到0.000 1）
			</span>
			<span class="btn-box" @click="hadleAnswer(49)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<iframe src="https://www.geogebra.org/scientific" frameborder="0" class="iframe-box"></iframe>
			<div v-if="isShowAnswer49" >
			<p>
			<span class="zt-ls"><b>解</b></span> 因为<math display="0">
			<mi>α</mi>
			<mo>∈</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">[</mo>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo>,</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">]</mo>
			</mrow>
			</math>，所以<i>α</i>在<i>y</i>=sin <i>α</i>的一个单调区间内，这时使sin
			<i>α</i>=0.943 7的角<i>α</i>的值是唯一的.
			</p>
			<p>
			先将科学计算器的精确度设置为0.000
			1，再将科学计算器设置为弧度计算模式，然后依次按键：
			</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0214-4.jpg" />
			</p>
			<p>结果显示：</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0214-5.jpg" />
			</p>
			<p>所以　<i>α</i>≈1.233 6.</p>
			</div>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例2</b></span>　已知cos <i>α</i>=0.694
			3，0°≤<i>α</i>≤180°，求<i>α</i>的值.（结果精确到0.000 1）
			</span>
			<span class="btn-box" @click="hadleAnswer(50)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer50" >
			<p>
			<span class="zt-ls"><b>解</b></span>　因为0°≤<i>α</i>≤180°，所以<i>α</i>在<i>y</i>=cos
			<i>α</i>的一个单调区间内，这时使cos <i>α</i>=0.694
			3的角<i>α</i>的值是唯一的.
			</p>
			<p>
			先将科学计算器的精确度设置为0.000
			1，再将科学计算器设置为角度计算模式，然后依次按键：
			</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0215-1.jpg" />
			</p>
			<p>结果显示：</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0215-2.jpg" />
			</p>
			<p>所以<i>α</i>≈46.028 5°.</p>
			<p>
			注意：应当区分所给条件中角的单位是角度还是弧度.如果是角度，计算时应用角度计算模式；
			如果是弧度，计算时应用弧度计算模式.
			</p>
			</div>
			</div>
			</div>
			</div>
			<!-- 204 -->
			@@ -688,11 +7706,121 @@
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>

			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例3</b></span>　已知tan <i>α</i>=-2.747 0，<math display="0">
			<mi>α</mi>
			<mo>∈</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo>,</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>，求<i>α</i>的值.（结果精确到0.000 1）
			</span>
			<span class="btn-box" @click="hadleAnswer(51)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</p>
			<iframe src="https://www.geogebra.org/scientific" frameborder="0" class="iframe-box"></iframe>
			<div v-if="isShowAnswer51" >
			<p>
			<span class="zt-ls"><b>解</b></span> 因为<math display="0">
			<mi>α</mi>
			<mo>∈</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>−</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo>,</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>，所以<i>α</i>在<i>y</i>=tan <i>α</i>的一个单调区间内，这时使tan
			<i>α</i>=-2.747 0的角<i>α</i>的值是唯一的.
			</p>
			<p>
			先将科学计算器的精确度设置为0.000
			1，再将科学计算器设置为弧度计算模式，然后依次按键：
			</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0215-5.jpg" />
			</p>
			<p>结果显示：</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0215-6.jpg" />
			</p>
			<p>所以　<i>α</i>≈-1.221 7.</p>
			</div>
			<p class="p-btn" >
			<span>
			<span class="zt-ls"><b>例4</b></span>　已知sin <i>α</i>=-0.857
			2，<i>α</i>∈［0，2π］，求<i>α</i>的值.（结果精确到0.000 1）
			</span>
			<span class="btn-box" @click="hadleAnswer(52)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			<span class="btn-box" @click="openDialog(thinkOne)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
			<path class="a"
			d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
			transform="translate(-3761 14334.001)" />
			</svg>
			</span>
			</p>
			<div v-if="isShowAnswer52" >
			<p>
			<span class="zt-ls"><b>解</b></span>
			先将科学计算器的精确度设置为0.000
			1，再将科学计算器设置为弧度计算模式，然后依次按键：
			</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0215-7.jpg" />
			</p>
			<p>结果显示：</p>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0215-8.jpg" />
			</p>
			<p>即</p>
			<p class="center">sin 1.029 8≈0.857 2.</p>
			<p>因为</p>
			<p class="center">sin（π+1.029 8）=-sin 1.029 8≈-0.857 2，</p>
			<p>所以符合条件的第三象限角是π+1.029 8≈4.171 4.</p>
			<p>因为</p>
			<p class="center">sin（2π-1.029 8）=-sin 1.029 8≈-0.857 2，</p>
			<p>所以符合条件的第四象限角是2π-1.029 8≈5.253 4.</p>
			<p>
			所以满足sin <i>α</i>=-0.857
			2，<i>α</i>∈［0，2π］的角<i>α</i>的集合为{4.171 4，5.253 4}.
			</p>
			</div>
			</div>
			</div>
			</div>

			<!-- 205 -->
			<div class="page-box" page="212">
			<div v-if="showPageList.indexOf(212) > -1">
			@@ -701,25 +7829,28 @@
			<p>第五单元三角函数</p>
			</li>
			<li>
			<p><span>205</span></p>
			<p><span>205-206</span></p>
			</li>
			</ul>

			<div class="padding-116"></div>
			<div class="padding-116">
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[212] ? questionData[212][1] : []" :hideCollect="true"
			sourceType="json" inputBc="#d3edfa" v-if="questionData"></examinations>
			</div>
			<h3 id="c066">习题5.8<span class="fontsz2">＞＞＞</span></h3>
			<div class="bj">
			<examinations :cardList="questionData[212] ? questionData[212][2] : []" :hideCollect="true"
			sourceType="json" inputBc="#d3edfa" v-if="questionData"></examinations>
			</div>
			</div>
			</div>
			</div>

			<!-- 206 -->
			<div class="page-box" page="213">
			<div v-if="showPageList.indexOf(213) > -1">
			<ul class="page-header-odd fl al-end">
			<li>206</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			</div>
			</div>
			<div class="page-box hidePage" page="213"></div>

			<!-- 207 -->
			<div class="page-box" page="214">
			@@ -733,7 +7864,34 @@
			</li>
			</ul>

			<div class="padding-116"></div>
			<div class="padding-116">
			<h2 id="b038">
			数学园地<span class="fontsz1">＞＞＞＞＞＞＞＞</span>
			</h2>
			<p class="center">三角学在我国的发展</p>
			<p>
			我国很早就开始了对三角知识的研究.我国古老的数学书籍《周髀算经》一书中，记载了古时候人们计算地面上一点到太阳距离的方法.魏晋时期的著名数学家刘徽在古人“重差术”的基础上，编撰了《海岛算经》一书.
			</p>
			<p>
			春秋时期的《考工记》一书，对“角”已有初步认识，并用“倨句”表示角度的多少，其中直角叫作“矩”.
			</p>
			<p>
			唐朝开元六年至十四年（718—726），唐代文学家翟昙悉达修撰《开元占经》一百二十卷，将印度数学家编制的三角函数表载于其中，这是传入我国的最早的三角函数表.
			</p>
			<p>
			由我国著名数学家徐光启（1562—1633）等人共同编译的《大测》二卷序言中说：“大测者，测三角之法也.”我国“三角学”一词即由此而来.该书介绍了三角函数值的造表方法和正弦定理、余弦定理等.
			</p>
			<p>
			明末清初数学家薛凤祚著有《三角算法》一书，这是我国数学家自己撰写的第一部三角学著作.书中所介绍的三角学知识，要比《大测》《测量全义》中的内容更详细与完备.
			</p>
			<p>
			清初著名数学家梅文鼎研究三角学数年，对所传入的三角学知识进行了通俗的解释，并著有《平三角举要》五卷.其内容由浅入深，循序渐进，条理清楚，是当时以及后人学习三角学的主要教科书.
			</p>
			<p>
			如果想知道更多的关于三角学在我国发展历程中所经历的人和事，你可以通过不同的途径（如上网搜索）查找资料，整理出更为丰富的史料来.对此，你不妨与同学合作，试一试.
			</p>
			<p>——摘录自沈文选、杨清桃编著的《数学史话览胜》一书，引用时有改动</p>
			</div>
			</div>
			</div>

			@@ -745,7 +7903,182 @@
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<h2 id="b039">
			单元小结<span class="fontsz1">＞＞＞＞＞＞＞＞</span>
			</h2>
			<p class="bj2"><b>学习导图</b></p>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0219-1.jpg" />
			</p>
			<p class="bj2"><b>学习指导</b></p>
			<p>
			1.与角<i>α</i>终边相同的角的集合：<i>S</i>={<i>β</i>\|<i>β</i>=<i>α</i>+<i>k</i>·2π，<i>k</i>∈<b>Z</b>}.
			</p>
			<p>2.弧度与角度的换算.</p>
			<math display="block">
			<mtable columnspacing="1em" rowspacing="4pt">
			<mtr>
			<mtd>
			<mi>π</mi>
			<mo>=</mo>
			<msup>
			<mn>180</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>;</mo>
			<mn>2</mn>
			<mi>π</mi>
			<mo>=</mo>
			<msup>
			<mn>360</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>.</mo>
			</mtd>
			</mtr>
			<mtr>
			<mtd>
			<mn>1</mn>
			<mrow>
			<mi mathvariant="normal">r</mi>
			<mi mathvariant="normal">a</mi>
			<mi mathvariant="normal">d</mi>
			</mrow>
			<mo>=</mo>
			<mfrac>
			<msup>
			<mn>180</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mi>π</mi>
			</mfrac>
			<mo>≈</mo>
			<msup>
			<mn>57.30</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>=</mo>
			<msup>
			<mn>57</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<msup>
			<mn>18</mn>
			<mrow>
			<mi data-mjx-alternate="1" mathvariant="normal">′</mi>
			</mrow>
			</msup>
			<mo>;</mo>
			<msup>
			<mn>1</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>=</mo>
			<mfrac>
			<mi>π</mi>
			<mn>180</mn>
			</mfrac>
			<mrow>
			<mi mathvariant="normal">r</mi>
			<mi mathvariant="normal">a</mi>
			<mi mathvariant="normal">d</mi>
			</mrow>
			<mo>≈</mo>
			<mn>0.01745</mn>
			<mrow>
			<mi mathvariant="normal">r</mi>
			<mi mathvariant="normal">a</mi>
			<mi mathvariant="normal">d</mi>
			</mrow>
			<mo>.</mo>
			</mtd>
			</mtr>
			</mtable>
			</math>
			<p>
			3.弧长公式为<i>l</i>=<i>αr</i>，扇形的面积公式为<math display="0">
			<mi>S</mi>
			<mo>=</mo>
			<mfrac>
			<mn>1</mn>
			<mn>2</mn>
			</mfrac>
			<mi>r</mi>
			<mi>l</mi>
			</math>.
			</p>
			<p>4.任意角的正弦、余弦和正切.</p>
			<p>
			点<i>P</i>（<i>x</i>，<i>y</i>）是角<i>α</i>的终边上异于原点的任意一点，点<i>P</i>到原点的距离为<math display="0">
			<mi>r</mi>
			<mo>=</mo>
			<msqrt>
			<msup>
			<mi>x</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			<mo>+</mo>
			<msup>
			<mi>y</mi>
			<mrow>
			<mn>2</mn>
			</mrow>
			</msup>
			</msqrt>
			<mo>></mo>
			<mn>0</mn>
			</math>，则<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mi>y</mi>
			<mi>r</mi>
			</mfrac>
			</math>，<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mi>x</mi>
			<mi>r</mi>
			</mfrac>
			</math>，<math display="0">
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mi>y</mi>
			<mi>x</mi>
			</mfrac>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mi>x</mi>
			<mo>≠</mo>
			<mn>0</mn>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>.
			</p>
			</div>
			</div>
			</div>
			<!-- 209 -->
			@@ -759,59 +8092,218 @@
			<p><span>209</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<p>5.任意角的正弦函数、余弦函数和正切函数.</p>
			<p>正弦函数 <i>y</i>=sin <i>x</i>，<i>x</i>∈<b>R</b>；</p>
			<p>余弦函数 <i>y</i>=cos <i>x</i>，<i>x</i>∈<b>R</b>；</p>
			<p>
			正切函数 <i>y</i>=tan <i>x</i>，<math display="0">
			<mi>x</mi>
			<mo>≠</mo>
			<mfrac>
			<mi>π</mi>
			<mn>2</mn>
			</mfrac>
			<mo>+</mo>
			<mi>k</mi>
			<mi>π</mi>
			<mo stretchy="false">(</mo>
			<mi>k</mi>
			<mo>∈</mo>
			<mrow>
			<mi mathvariant="bold">Z</mi>
			</mrow>
			<mo stretchy="false">)</mo>
			</math>.
			</p>
			<p>6.同角三角函数基本关系式.</p>
			<p>
			（1）平方关系：sin <sup>2</sup> <i>α</i>+cos <sup>2</sup>
			<i>α</i>=1；
			</p>
			<p>
			（2）商数关系：<math display="0">
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			</mrow>
			<mrow>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mi>α</mi>
			</mrow>
			</mfrac>
			</math>.
			</p>
			<p>7.诱导公式表（<i>k</i>∈<b>Z</b>）.</p>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0220-3.jpg" />
			</p>
			<p>8.正弦函数、余弦函数的图像和性质.</p>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0220-4.jpg" />
			</p>
			</div>
			</div>
			</div>
			<!-- 210 -->

			<div class="page-box" page="217">
			<div v-if="showPageList.indexOf(217) > -1">
			<ul class="page-header-odd fl al-end">
			<li>210</li>
			<li>210-211</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116"></div>
			<div class="padding-116">
			<h2 id="b040">
			单元检测<span class="fontsz1">＞＞＞＞＞＞＞＞</span>
			</h2>
			<div class="bj">
			<examinations :cardList="questionData[217]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
			</div>
			</div>
			</div>
			</div>
			<!-- 211 -->
			<div class="page-box" page="218">
			<div v-if="showPageList.indexOf(218) > -1">
			<ul class="page-header-box">
			<li>
			<p>第五单元三角函数</p>
			</li>
			<li>
			<p><span>211</span></p>
			</li>
			</ul>
			<div class="padding-116"></div>
			<div class="page-box hidePage" page="218"></div>
			<!-- 解题思路弹窗 -->
			<el-dialog :visible.sync="thinkingDialog" width="40%" :append-to-body="true" :show-close="false"
			@close="closeDialog" class="thinkDialog">
			<div slot="title" class="think-header"
			style="padding: 0; text-align: center; color: #333;display:flex;justify-content: center;">
			<span style=""> 分析 </span>
			<svg style="position: absolute; right:10px;cursor: pointer;" @click="thinkingDialog = false" t="1718596022986"
			class="icon" viewBox="0 0 1024 1024" version="1.1" xmlns="http://www.w3.org/2000/svg" p-id="4252" width="20"
			height="20" xmlns:xlink="http://www.w3.org/1999/xlink">
			<path
			d="M176.661601 817.172881C168.472798 825.644055 168.701706 839.149636 177.172881 847.338438 185.644056 855.527241 199.149636 855.298332 207.338438 846.827157L826.005105 206.827157C834.193907 198.355983 833.964998 184.850403 825.493824 176.661601 817.02265 168.472798 803.517069 168.701706 795.328267 177.172881L176.661601 817.172881Z"
			fill="#979797" p-id="4253"></path>
			<path
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			fill="#979797" p-id="4254"></path>
			</svg>
			</div>
			</div>


			<ul>
			<li v-for="(item, index) in thinkData" :key="index">
			<div v-if="index <= showIndex" style="display: flex">
			<span style="position: relative">
			<span style="position: absolute; top: 16px; left: 13px; color: #fff">{{ index + 1 }}</span>
			<img src="../../assets/images/icon/blue-group.png" alt="" style="margin-right: 10px"
			v-if="index < thinkOne.length - 1" />
			<img src="../../assets/images/icon/blue.png" alt="" v-if="index == thinkOne.length - 1"
			style="margin-right: 10px" />
			</span>
			<p class="txt-p" v-html="item"></p>
			</div>
			</li>
			</ul>
			<div @click="changeNext" style="
			display: flex;
			flex-direction: column;
			align-items: center;
			justify-content: center;
			">
			<img src="../../assets/images/icon/mouse.png" alt="" v-if="showIndex < thinkData.length - 1" />
			<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" t="1710234570135"
			class="icon" viewBox="0 0 1024 1024" version="1.1" p-id="5067" width="15" height="15">
			<path
			d="M2.257993 493.371555 415.470783 906.584344 512 1003.113561 608.529217 906.584344 1021.742007 493.371555 925.212789 396.842337 512 810.055127 98.787211 396.842337Z"
			fill="#1296db" p-id="5068" />
			<path
			d="M2.257993 117.980154 415.470783 531.192944 512 627.722161 608.529217 531.192944 1021.742007 117.980154 925.212789 21.450937 512 434.663727 98.787211 21.450937Z"
			fill="#1296db" p-id="5069" />
			</svg>
			</div>
			</el-dialog>
			</div>
			</template>

			<script>
			import paint from '@/components/paint/index.vue'
			import examinations from "@/components/examinations/index.vue";
			import fillInTable from "@/components/fillInTable/index.vue";
			const handleShow = (num) => {
			const obj = {}
			for (let index = 0; index < num; index++) {
			obj['isShowAnswer' + index] = false
			}
			return obj
			}
			const showObj = handleShow(60)
			export default {
			name: '',
			name: "",
			props: {
			showPageList: {
			type: Array,
			default: [],
			},
			questionData: {
			type: Object,
			},
			},
			components: {},
			components: { examinations, fillInTable,paint },
			data() {
			return {}
			return {
			...showObj,
			isShowAnswer:false,
			queryDataOne: {
			stemTxt:"完成下表，并利用“五点法”画出<i>y</i>=3sin <i>x</i>在区间［0，2π］内的简图，并说明<i>y</i>=3sin <i>x</i>的图像与正弦函数<i>y</i>=sin <i>x</i>的图像的区别和联系.",
			showData: [
			["<i>x</i>", "0", '<math display="block"><mfrac><mn>1</mn><mn>2</mn></mfrac></math>', "1", '<math display="block"><mfrac><mn>3</mn><mn>2</mn></mfrac></math>', "2"],
			["<i>y</i>=sin <i>x</i>", "0", "1", "0", "-1", "0"],
			["<i>y</i>=3sin <i>x</i>", "", "", "", "", ""],
			],
			answer:"0,3,0,-3,0"
			},
			queryDataTwo:{
			stemTxt:"完成下表，利用“五点法”画出y=1-cos x在区间［0，2π］内的简图，并说明y=1-cos x的图像与y=cos x的图像的区别和联系.",
			showData: [
			["x", "0", '<math display="block"><mfrac><mi>π</mi><mn>2</mn></mfrac></math>', "1", "3/2", "2"],
			["y=cosx", "", "", "", "", ""],
			["y=1-cosx", "", "", "", "", ""],
			],
			answer:"<p>1,0,-1,0,1</p><p>0,1,2,1,0</p>"
			},
			showIndex:0,
			thinkingDialog: false,
			thinkData:[],
			thinkOne:[
			'因为sin <i>α</i>=-0.8572＜0，在［0，2π］范围内有两个<i>α</i>值满足条件，它们分别位于第三象限和第四象限，即<i>α</i>在［π，2π］范围内.可用科学计算器先求出sin<i>α</i>=0.857 2所对应的锐角，再利用诱导公式求出所求的角.'
			]
			}
			},
			computed: {},
			watch: {},
			created() { },
			mounted() { },
			methods: {},
			methods:{
			hadleAnswer(index) {
			this['isShowAnswer' + index] = !this['isShowAnswer' + index]
			},
			openDialog(queryData) {
			this.thinkData = queryData
			this.thinkingDialog = !this.thinkingDialog
			},
			closeDialog() {
			this.showIndex = 0
			},
			changeNext() {
			if (this.showIndex < this.thinkData.length - 1) this.showIndex = this.showIndex + 1
			}
			}
			}
			</script>

			<style lang="less" scoped></style>
			<style lang="less" scoped>
			.table-answer-box {
			padding: 4px;
			border: 1px solid #00adee;
			display: flex;
			}
			li {
			list-style: none;
			}
			</style>