testbookLayout.git

			@@ -1,5 +1,5 @@
			<template>
			<div class="chapter" num="5">
			<div class="chapter" num="6">
			<!-- 第五单元首页 -->
			<div class="page-box" page="160">
			<div v-if="showPageList.indexOf(160) > -1">
			@@ -174,18 +174,39 @@
			<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="center">
			<img class="img-c" alt="" src="../../assets/images/0168-1.jpg" />
			<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>
			<p class="img">图5-4</p>
			<p>（1） 225°；（2） -300°.</p>
			<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.
			<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>
			（2）
			<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>
			@@ -233,7 +254,7 @@
			<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">
			@@ -256,57 +277,107 @@
			<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>（1） 600°；（2） -230°；（3） -890°.</p>
			<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>
			（2）
			<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>
			（3）
			<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>（1）终边在<i>y</i>轴正半轴上的角的集合；</p>
			<p>（2）终边在<i>y</i>轴负半轴上的角的集合；</p>
			<p>（3）终边在<i>y</i>轴上的角的集合.</p>
			<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 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>
			<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>}.
			<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>
			<p>（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>}.
			<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>
			</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">
			<p>（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 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>
			@@ -316,6 +387,9 @@
			</div>
			</div>
			</div>
			</div>
			<!-- 160 -->
			<div class="page-box hidePage" page="167">
			</div>
			<!-- 161 -->
			<div class="page-box" page="168">
			@@ -328,7 +402,6 @@
			<p><span>161</span></p>
			</li>
			</ul>

			<div class="padding-116">
			<h3 id="c050">习题5.1<span class="fontsz2">＞＞＞</span></h3>
			<div class="bj">
			@@ -572,90 +645,106 @@
			<img class="img-c" alt="" src="../../assets/images/0174-6.jpg" />
			</p>
			<p class="img">图5-8</p>
			<p>
			<span class="zt-ls"><b>例1</b></span>　把下列各角化为弧度.
			<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>
			<p>
			<span class="zt-ls"><b>解</b></span>
			</p>
			<p class="left1">
			<math display="">
			<mo stretchy="false">（1）</mo>
			<msup>
			<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>
			<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>
			<mo>×</mo>
			<mfrac>
			<mi>π</mi>
			</mrow>
			<mn>4</mn>
			</mfrac>
			<mo>.</mo>
			</math>
			</p>
			<p class="left1">
			<math display="">
			<mo stretchy="false">（3）</mo>
			<msup>
			<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>
			<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>
			<p>
			<span class="zt-ls"><b>例2</b></span>　把下列各角化为角度.
			<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）
			@@ -669,71 +758,73 @@
			</mfrac>
			</math>；（2） 5rad（结果精确到0.01）.
			</p>
			<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>
			<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>180</mn>
			<mn>60</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mn>3</mn>
			</mfrac>
			<mo>=</mo>
			<mo>−</mo>
			<msup>
			<mn>60</mn>
			<mo>.</mo>
			</math>
			</p>
			<p class="left1">
			<math display="">
			<mo stretchy="false">（2）</mo>
			<mn>5</mn>
			<mrow>
			<mo>∘</mo>
			<mi mathvariant="normal">r</mi>
			<mi mathvariant="normal">a</mi>
			<mi mathvariant="normal">d</mi>
			</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>
			<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>180</mn>
			<mn>286.44</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 class="bk">
			<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" />
			@@ -758,35 +849,59 @@
			<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>（1） -5.6；（2） 154°13′.</p>
			<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 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>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0175-3.jpg" />
			<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>
			<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>
			<p>
			（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 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>
			<calculator />
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			@@ -992,78 +1107,89 @@
			<p class="center">
			<img class="img-d" alt="" src="../../assets/images/0176-11.jpg" />
			</p>
			<p>
			<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）.
			<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>
			<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>
			<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>3</mn>
			<mi>π</mi>
			<mn>1200</mn>
			<mo>×</mo>
			<mn>5</mn>
			</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>
			<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>
			</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>
			<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>
			@@ -1080,99 +1206,110 @@
			<img class="img-c" alt="" src="../../assets/images/0177-1.jpg" />
			</p>
			<p class="img">图5-10</p>
			<p>
			<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>）
			<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>
			<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>
			<div v-if="isShowAnswer13" >
			<p>
			<span class="zt-ls"><b>解</b></span> 由于<math display="0">
			<msup>
			<mn>60</mn>
			<mrow>
			<mtext> </mtext>
			<mi mathvariant="normal">c</mi>
			<mi mathvariant="normal">m</mi>
			<mo>∘</mo>
			</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>
			</msup>
			<mo>=</mo>
			<mfrac>
			<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>
			<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>
			@@ -1509,7 +1646,6 @@
			</div>
			</div>
			</div>

			<!-- 169 -->
			<div class="page-box" page="176">
			<div v-if="showPageList.indexOf(176) > -1">
			@@ -1522,105 +1658,116 @@
			</li>
			</ul>
			<div class="padding-116">
			<p>
			<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.
			<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>
			<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 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>
			@@ -1650,7 +1797,6 @@
			</div>
			</div>
			</div>

			<!-- 170 -->
			<div class="page-box" page="177">
			<div v-if="showPageList.indexOf(177) > -1">
			@@ -1754,9 +1900,114 @@
			<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>
			（1） sin（-210°）；（2） tan760°；（3）
			<math display="0">
			<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>
			@@ -1766,84 +2017,23 @@
			</mrow>
			<mn>12</mn>
			</mfrac>
			</math>.
			</p>
			<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>
			<p>
			（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>
			<p>
			（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，
			<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>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>
			<p>
			<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.
			</p>
			<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>
			@@ -1960,128 +2150,153 @@
			<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>
			<span class="zt-ls"><b>例4</b></span>　求5sin180°-4sin90°+2tan180°-7sin270°的值.
			</p>
			<p>
			<span class="zt-ls"><b>解</b></span> 5sin 180°-4sin 90°+2 tan
			180°-7sin 270°
			<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>
			<p>=5×0-4×1+2×0-7×（-1）</p>
			<p>=3.</p>
			<p>
			<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>
			<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>
			</mrow>
			<mn>2</mn>
			</mfrac>
			</math>的值.
			</p>
			<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>
			<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>
			<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>
			</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" >

			<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>
			@@ -2144,10 +2359,8 @@
			</div>
			</div>
			</div>

			<!-- 174 -->
			<div class="page-box hidePage" page="181"></div>

			<!-- 175 -->
			<div class="page-box" page="182">
			<div v-if="showPageList.indexOf(182) > -1">
			@@ -2156,7 +2369,7 @@
			<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">
			@@ -2229,114 +2442,125 @@
			</mfrac>
			</math>.
			</p>
			<p>
			<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.
			<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>
			<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>
			<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>
			</msqrt>
			<mo>=</mo>
			<mo>−</mo>
			<msqrt>
			<mn>1</mn>
			<mo>=</mo>
			<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>
			<msqrt>
			<mn>1</mn>
			<mo>−</mo>
			<mfrac>
			<mn>4</mn>
			<mn>5</mn>
			</mfrac>
			</mrow>
			<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>3</mn>
			<mn>4</mn>
			<mn>5</mn>
			</mfrac>
			</mfrac>
			<mo>=</mo>
			<mo>−</mo>
			<mfrac>
			<mn>4</mn>
			<mn>3</mn>
			</mfrac>
			<mo>.</mo>
			</mtd>
			</mtr>
			</mtable>
			</math>
			<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">
			@@ -2382,8 +2606,33 @@
			</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>
			<span class="zt-ls"><b>例2</b></span>　已知<math display="0">
			<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>
			@@ -2392,179 +2641,151 @@
			<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.
			</p>
			<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>
			<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>
			<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>12</mn>
			<mn>5</mn>
			<mn>13</mn>
			</mfrac>
			</math>.
			</p>
			</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">
			<p>
			<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>
			@@ -2577,388 +2798,100 @@
			</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>
			<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>5</mn>
			<mn>12</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>
			<p>
			<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.
			</p>
			<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>
			<p>
			<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>.
			</p>
			<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 class="bk">
			<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>
			<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.
			</p>
			<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>
			</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>
			<p>方法二：</p>
			<p class="left1">
			<math display="">
			<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>
			@@ -2991,12 +2924,7 @@
			<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"
			<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>
			@@ -3093,11 +3021,340 @@
			</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 hidePage" page="183">
			</div>
			<!-- 177 -->
			<div class="page-box" page="184">
			<div v-if="showPageList.indexOf(184) > -1">
			@@ -3125,7 +3382,6 @@
			</div>
			</div>
			</div>

			<!-- 178 -->
			<div class="page-box" page="185">
			<div v-if="showPageList.indexOf(185) > -1">
			@@ -3298,7 +3554,6 @@
			</div>
			</div>
			</div>

			<!-- 179 -->
			<div class="page-box" page="186">
			<div v-if="showPageList.indexOf(186) > -1">
			@@ -3310,126 +3565,134 @@
			<p><span>179</span></p>
			</li>
			</ul>

			<div class="padding-116">
			<p>
			<span class="zt-ls"><b>例1</b></span>　求下列三角函数的值.
			<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>
			（1）
			<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>5</mn>
			<mn>13</mn>
			<mi>π</mi>
			</mrow>
			<mn>3</mn>
			<mn>6</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>；（3） tan 405°.
			</p>
			<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>
			</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>
			<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>
			</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>
			<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>
			<mo>=</mo>
			<mfrac>
			<mrow>
			<mn>5</mn>
			<mi>π</mi>
			</mrow>
			<mn>3</mn>
			<mn>1</mn>
			<mn>2</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>
			</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>
			<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>
			<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>
			@@ -3696,8 +3959,15 @@
			</li>
			</ul>
			<div class="padding-116">
			<p>
			<span class="zt-ls"><b>例2</b></span>　求下列三角函数的值.
			<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）
			@@ -3713,190 +3983,192 @@
			</mfrac>
			</math>；（3） tan 570°.
			</p>
			<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>
			<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>180</mn>
			<mn>225</mn>
			<mrow>
			<mo>∘</mo>
			</mrow>
			</msup>
			<mo>+</mo>
			<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 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>
			<mo>=</mo>
			<mo>−</mo>
			<mfrac>
			<msqrt>
			<mn>2</mn>
			</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>
			</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>
			<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>
			<mo>=</mo>
			<mo>−</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</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>
			<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>
			</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>
			<mo>=</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</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>
			<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>
			</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>
			<mo>=</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</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>
			</mtd>
			</mtr>
			<mtr>
			<mtd></mtd>
			<mtd>
			<mi></mi>
			<mo>=</mo>
			<mfrac>
			<msqrt>
			<mn>3</mn>
			</msqrt>
			<mn>3</mn>
			</msqrt>
			<mn>3</mn>
			</mfrac>
			</mtd>
			</mtr>
			</mtable>
			</math>
			</p>
			</mfrac>
			</mtd>
			</mtr>
			</mtable>
			</math>
			</p>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			@@ -4113,8 +4385,15 @@
			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>
			<span class="zt-ls"><b>例3</b></span>　求下列三角函数的值.
			<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）
			@@ -4133,123 +4412,140 @@
			<mo stretchy="false">)</mo>
			</math>.
			</p>
			<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>
			<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 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>
			<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 data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>=</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<msup>
			<mn>390</mn>
			<mrow>
			<mo>∘</mo>
			<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>
			</msup>
			<mo>=</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">(</mo>
			<mo>=</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</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>
			<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>
			@@ -4257,28 +4553,28 @@
			</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>
			<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>
			<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>
			<mo>=</mo>
			<mo>−</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>4</mn>
			@@ -4286,60 +4582,45 @@
			</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>
			</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>
			<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>
			<mo>=</mo>
			<mo>−</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</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>
			<mo>=</mo>
			<mo>−</mo>
			<msqrt>
			<mn>3</mn>
			</msqrt>
			</mtd>
			</mtr>
			</mtable>
			</math>
			</p>
			</div>
			</div>
			</div>
			</div>
			@@ -4458,8 +4739,15 @@
			<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>
			<span class="zt-ls"><b>例4</b></span>　求下列三角函数的值.
			<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）
			@@ -4486,78 +4774,94 @@
			</mfrac>
			</math>.
			</p>
			<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>
			<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>180</mn>
			<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 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>
			<mo>=</mo>
			<mo>−</mo>
			<mfrac>
			<msqrt>
			<mn>2</mn>
			</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>
			</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>
			<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>
			<mo>=</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>2</mn>
			@@ -4565,67 +4869,67 @@
			</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>
			<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>
			<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>
			<mo>−</mo>
			<mi>tan</mi>
			<mo data-mjx-texclass="NONE">⁡</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>
			<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>
			<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>
			<mo>=</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<mn>3</mn>
			@@ -4633,226 +4937,223 @@
			</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>
			<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>
			<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>
			<mo>−</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</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>
			<mo>=</mo>
			<mo>−</mo>
			<mfrac>
			<msqrt>
			<mn>2</mn>
			</msqrt>
			<mn>2</mn>
			</msqrt>
			<mn>2</mn>
			</mfrac>
			<mo>.</mo>
			</math>
			</p>
			<p>
			<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>
			</p>
			<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>
			</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>
			<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>
			<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>
			<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>
			<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>
			</mtd>
			</mtr>
			</mtable>
			</math>
			<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：
			@@ -4871,7 +5172,7 @@
			<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">
			@@ -4905,121 +5206,147 @@
			<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>
			（1） sin 63°52′41″；（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）
			<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>
			<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>6</mn>
			<mn>4</mn>
			<mi>π</mi>
			</mrow>
			<mn>5</mn>
			<mn>3</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>.
			</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>
			</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">
			<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>
			<p>
			（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>
			<p>
			（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>
			<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>6</mn>
			<mn>4</mn>
			<mi>π</mi>
			</mrow>
			<mn>5</mn>
			<mn>3</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo>≈</mo>
			<mo>−</mo>
			<mn>0.73</mn>
			<mo>.</mo>
			</math>
			<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>
			@@ -5029,6 +5356,9 @@
			</div>
			</div>
			</div>
			</div>
			<!-- 186 -->
			<div class="page-box hidePage" page="193">
			</div>
			<!-- 187 -->
			<div class="page-box" page="194">
			@@ -5230,33 +5560,59 @@
			<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>（1） <i>y</i>=-sin<i>x</i>；（2） <i>y</i>=1+sin<i>x</i>.</p>
			<p>
			<span class="zt-ls"><b>解</b></span>（1）列表（表5-6）.
			<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>
			<p class="img">表5-6</p>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0201-2.jpg" />
			<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>
			<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>
			<p>（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 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>
			@@ -5371,177 +5727,215 @@
			<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>
			<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.
			<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>
			<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 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>（1） <i>y</i>=3+sin<i>x</i>；（2） <i>y</i>=-2sin<i>x</i>.</p>
			<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 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>
			<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>
			<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>
			<mstyle scriptlevel="0">
			<mspace width="thinmathspace"></mspace>
			</mstyle>
			<mo data-mjx-texclass="OPEN">{</mo>
			<mi>x</mi>
			<mo>=</mo>
			<mn>2</mn>
			<mi>k</mi>
			<mi>π</mi>
			<mo>−</mo>
			<mfrac>
			<mi>π</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>
			</mfrac>
			<mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
			<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>
			<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>
			<p>
			（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>
			</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>
			<mstyle scriptlevel="0">
			<mspace width="thinmathspace"></mspace>
			</mstyle>
			<mo data-mjx-texclass="OPEN">{</mo>
			<mi>x</mi>
			<mo>=</mo>
			<mn>2</mn>
			<mi>k</mi>
			<mi>π</mi>
			<mo>−</mo>
			<mfrac>
			<mi>π</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>
			</mfrac>
			<mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
			<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>
			<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.
			</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>
			<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>
			<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>
			<mstyle scriptlevel="0">
			<mspace width="thinmathspace"></mspace>
			</mstyle>
			<mo data-mjx-texclass="OPEN">{</mo>
			<mi>x</mi>
			<mo>=</mo>
			<mn>2</mn>
			<mi>k</mi>
			<mi>π</mi>
			<mo>+</mo>
			<mfrac>
			<mi>π</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>
			</mfrac>
			<mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
			<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>
			<mo>,</mo>
			<mi>k</mi>
			<mo>∈</mo>
			<mrow>
			<mi mathvariant="bold">Z</mi>
			</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>
			<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>
			</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>
			@@ -5666,94 +6060,62 @@
			<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>
			（1）<math display="0">
			<mi>sin</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mrow>
			<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>
			<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>；（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>.
			</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>
			<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>
			<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>
			<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>
			@@ -5761,32 +6123,152 @@
			</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>
			</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>
			<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>
			</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>
			@@ -5803,69 +6285,6 @@
			<li>上册</li>
			</ul>
			<div class="padding-116">
			<p>
			（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>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			@@ -6022,20 +6441,57 @@
			<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>（1） <i>y</i>=2cos <i>x</i>；（2） <i>y</i>=-1+cos <i>x</i>.</p>
			<p>
			<span class="zt-ls"><b>解</b></span>（1）列表（表5-10）.
			<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="img">表5-10</p>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0207-5.jpg" />
			<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>
			<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>
			<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>
			@@ -6051,19 +6507,7 @@
			</li>
			</ul>
			<div class="padding-116">
			<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>

			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			@@ -6144,22 +6588,31 @@
			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>
			<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.
			<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>
			<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 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>
			@@ -6187,87 +6640,60 @@
			<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>
			（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>
			<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>
			<mi>π</mi>
			</mrow>
			<mn>4</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>
			<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>
			</math>与<math display="0">
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mfrac>
			<mi>π</mi>
			<mn>8</mn>
			<mrow>
			<mn>5</mn>
			<mi>π</mi>
			</mrow>
			<mn>4</mn>
			</mfrac>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>.
			</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>
			<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>
			<div v-if="isShowAnswer44" >
			<p>
			<span class="zt-ls"><b>解</b></span>（1）因为<math display="0">
			<mi>π</mi>
			<mo>,</mo>
			<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>
			@@ -6275,34 +6701,170 @@
			</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>
			</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>
			<mi>π</mi>
			</mrow>
			<mn>4</mn>
			</mfrac>
			<mo>.</mo>
			</math>
			<p>
			（2）<math display="0">
			</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">
			@@ -6314,14 +6876,7 @@
			</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">
			<mo><</mo>
			<mi>cos</mi>
			<mo data-mjx-texclass="NONE">⁡</mo>
			<mrow data-mjx-texclass="INNER">
			@@ -6333,86 +6888,9 @@
			</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>
			<mo>.</mo>
			</math>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			@@ -6707,22 +7185,31 @@
			</mfrac>
			</math>.
			</p>
			<p>
			<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>
			<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>
			</msqrt>
			<mn>2</mn>
			</mfrac>
			</math>，且<i>x</i>∈［0，2π］，求<i>x</i>的值.
			</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>
			<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>
			@@ -6835,95 +7322,106 @@
			</mfrac>
			</math>.
			</p>
			<p>
			<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>
			<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>
			<mfrac>
			<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>
			<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>
			<mo>,</mo>
			<mi>k</mi>
			<mo>∈</mo>
			<mrow>
			<mi mathvariant="bold">Z</mi>
			</mrow>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			<mo data-mjx-texclass="CLOSE">)</mo>
			</mrow>
			</math>，且0°≤<i>x</i>≤360°，求<i>x</i>的值.
			</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>
			<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>
			<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 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>
			<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">
			@@ -6942,8 +7440,9 @@
			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>
			<span class="zt-ls"><b>例3</b></span>　已知<math display="0">
			<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>
			@@ -6953,101 +7452,111 @@
			<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>
			<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>
			<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>
			<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>
			</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>
			@@ -7085,68 +7594,107 @@
			<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>
			<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）
			<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>
			<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.
			<calculator />
			<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>
			<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>
			<p>
			<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）
			</p>
			<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>
			<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>
			@@ -7158,98 +7706,118 @@
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>

			<div class="padding-116">
			<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 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>
			<p class="center">
			<img class="img-c" alt="" src="../../assets/images/0215-1.jpg" />
			<calculator />
			<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>
			<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>
			<p>
			<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）
			</p>
			<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>
			<p>
			<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）
			</p>
			<p class="block">
			<span class="zt-ls2"><b>分析</b></span>　因为sin <i>α</i>=-0.857
			2＜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.
			</p>
			<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>
			<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>
			@@ -7265,18 +7833,6 @@
			</li>
			</ul>
			<div class="padding-116">
			<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>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			@@ -7617,6 +8173,55 @@
			</div>
			<!-- 211 -->
			<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
			d="M795.328267 846.827157C803.517069 855.298332 817.02265 855.527241 825.493824 847.338438 833.964998 839.149636 834.193907 825.644055 826.005105 817.172881L207.338438 177.172881C199.149636 168.701706 185.644056 168.472798 177.172881 176.661601 168.701706 184.850403 168.472798 198.355983 176.661601 206.827157L795.328267 846.827157Z"
			fill="#979797" p-id="4254"></path>
			</svg>
			</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>

			@@ -7624,6 +8229,15 @@
			import paint from '@/components/paint/index.vue'
			import examinations from "@/components/examinations/index.vue";
			import fillInTable from "@/components/fillInTable/index.vue";
			import calculator from '@/components/calculator/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: "",
			props: {
			@@ -7635,9 +8249,10 @@
			type: Object,
			},
			},
			components: { examinations, fillInTable,paint },
			components: { examinations, fillInTable,paint,calculator },
			data() {
			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.",
			@@ -7656,10 +8271,30 @@
			["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.'
			]
			}
			},
			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>

			@@ -7669,4 +8304,7 @@
			border: 1px solid #00adee;
			display: flex;
			}
			li {
			list-style: none;
			}
			</style>