《高中数学正弦定理课件新人教必修》由会员分享，可在线阅读，更多相关《高中数学正弦定理课件新人教必修（38页珍藏版）》请在金锄头文库上搜索。
1、高中数学高中数学高中数学 必修必修必修5 5 5Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.1.上网活动：上网活动：“美丽的山河美丽的山河”图片搜索，感受图片搜索，感受到自然界的美。到自然
2、界的美。2.教师导语：自然界神奇美丽，要揭开其神秘教师导语：自然界神奇美丽，要揭开其神秘的面纱，需要借助于很多数学知识。的面纱，需要借助于很多数学知识。导入：导入：Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspos
3、e Pty Ltd.A AB BC 设点设点B B在珠江岸边，点在珠江岸边，点A A在对岸那边，为了测量在对岸那边，为了测量A A、B B两两点间的距离，你有何好办法呢？（给定你米尺和量器）点间的距离，你有何好办法呢？（给定你米尺和量器）Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Prof
4、ile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.A AB BC设问设问 若将点若将点C C移到如下图所示的位置，你还能求出移到如下图所示的位置，你还能求出A A、B B两点间的距离吗？两点间的距离吗？Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client
5、Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.正弦定理是什么？有哪些证明方法正弦定理是什么？有哪些证明方法？集体探究学习活动一：集体探究学习活动一：Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyr
6、ight 2004-2011 Aspose Pty Ltd.RTX讨论一：讨论一： 直角三角形中边角关系有直角三角形中边角关系有哪些？你能总结出一个式子哪些？你能总结出一个式子吗？这个式子对所有三角形吗？这个式子对所有三角形都适用吗？都适用吗？Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client P
7、rofile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.在RtABC中,各角与其对边的关系:不难得到:CBAabc数学建构数学建构Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011
8、Aspose Pty Ltd.在非直角三角形ABC中有这样的关系吗?AcbaCBEvaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.正弦定理在一个三角形中,各边和它所对角的正弦的比相等.即Eval
9、uation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.RTX讨论二：讨论二：正弦定理有哪些推导方法？正弦定理有哪些推导方法？Evaluation only.Created with Aspose.Slide
10、s for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.(1) 若直角三角形,已证得结论成立.所以AD=csinB=bsinC, 即同理可得DAcbCB图1过点A作ADBC于D,此时有证法1(2)若三角形是锐角三角形, 如图1,Evaluation only.Created wit
11、h Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.由(1)(2)(3)知，结论成立且仿(2)可得D(3) 若三角形是钝角三角形,且角C是钝角如图2, 此时也有交BC延长线于D,过点A作ADBC，CAcbB图2Evaluation only.Crea
12、ted with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.AcbCBDa利用向量的数量积，产生边的长与内角的三角函数的关系来证明.Evaluation only.Created with Aspose.Slides for .NET 3.5
13、Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation onl
14、y.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.RTX讨论三：讨论三： 以上证明方法体现了一种以上证明方法体现了一种什么样的数学思维规律？什么样的数学思维规律？ 答答 体现了由特殊到一般的体现了由特殊到一般的数学思维规律。数学思维规律。Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose
15、Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.1.利用正弦定理可以解决哪两类解利用正弦定理可以解决哪两类解斜三角形的问题？斜三角形的问题？2.在在“已知两边及其中一边对角已知两边及其中一边对角”解三角形问题中解的情况有几种？解三角形问题中解的情况有几种？集体探究学习活动二：集体探究学习活动二：Evaluation only.Created with Aspose.Slides for .NET 3.
16、5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.RTX讨论四：讨论四： 什么叫解三角形？利用正什么叫解三角形？利用正弦定理可以解决哪两类三角弦定理可以解决哪两类三角形的问题？形的问题？Evaluation only.Created with Aspose.Slides for .NET 3.5 Cl
17、ient Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.提醒提醒：三角形是由：三角形是由3条边和条边和3个角组成的，那么我们在运用个角组成的，那么我们在运用“正弦定理正弦定理”解三角形时，只需知道其中几个量，就可求解三角形时，只需知道其中几个量，就可求出余下的几个量？有没有前提条件？出余下的几个量？有没有前提条件？
18、结论结论 正弦定理的运用条件正弦定理的运用条件：1.已知三角形的两角及任一边；已知三角形的两角及任一边；2.已知三角形的两边已知三角形的两边及其一边所对的角及其一边所对的角。已知三角形的的某些边和角，求其他边和角的过程叫做已知三角形的的某些边和角，求其他边和角的过程叫做解三角形解三角形。数学建构数学建构Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspos
19、e.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.正弦定理有哪些方面的应用？正弦定理有哪些方面的应用？集体探究学习活动三：集体探究学习活动三：Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Clie
20、nt Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.例例1.ABCbc10数学应用：数学应用：Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty L
21、td.例例 2 已知已知a=16， b= ， A=30 解三角形。解三角形。解：由正弦定理解：由正弦定理得得所以所以6060, ,或或120120当当 时6060C=90C=30当当120120时时B16300ABC16316Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.
22、2.0.0.Copyright 2004-2011 Aspose Pty Ltd.变式变式: a=30, b=26, A=30求角求角B，C和边和边c300ABC2630解：由正弦定理解：由正弦定理得得所以所以25.725.70 0, ,C=180C=1800 0-A-B=124.3-A-B=124.30 0,a b A B ,三角形中大边对大角Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation o
23、nly.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.RTX讨论五：讨论五： 为什么在为什么在 “已知两边及其已知两边及其中一边对角中一边对角”解三角形问题解三角形问题中有一解、两解和无解三种中有一解、两解和无解三种情况？情况？Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty L
24、td.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.课堂练习课堂练习课本第课本第9页练习第页练习第2、3题题Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slide
25、s for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.RTX讨论六：讨论六： 已知两边及夹角，怎样求已知两边及夹角，怎样求三角形面积？三角形面积？Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Prof
26、ile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.证明：证明：BACDabc而而同理同理ha数学建构数学建构三角形面积公式：三角形面积公式：Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-
27、2011 Aspose Pty Ltd.RTX讨论七：讨论七： 正弦定理有哪些方面的应正弦定理有哪些方面的应用？用？Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.1000DACEB数学应用：
28、数学应用：Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.1000DACEB解解：过点过点D作作DE/AC交交BC于于E,于是，于是，答：山的高度约为答：山的高度约为811米。米。Evalua
29、tion only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.课堂练习课堂练习 做课本第做课本第11页第页第3题，求出题，求出上海东方明珠电视塔的高度，并上海东方明珠电视塔的高度，并上网查询验证。上网查询验证。Eval
30、uation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.解解：代入已知条件，得：代入已知条件，得：即即Evaluation only.Created with Aspose.Slides for .NET 3
31、.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation
32、only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.RTX探讨八：探讨八：请回顾本节课所学内容，并在请回顾本节课所学内容，并在RTX平台上展示平台上展示对本三连堂内容学生个人小结和集体小结：Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation onl
33、y.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.教师课堂总结教师课堂总结Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2
34、.0.0.Copyright 2004-2011 Aspose Pty Ltd.三角形中的边角关系正弦定理定理内容定理证明定理应用课堂总结课堂总结1.已已知知三三角角形形的的两两角角及及任任一一边边；2.已已知知三三角角形形的的两两边边及及其其一一边边所所对对的的角角。Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET
35、 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.课堂作业：课堂作业：1.课本第课本第10-11页页1、2、4、5、6题题;2.学习与评价第学习与评价第1、3页。页。Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Pr
36、ofile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd. 创新型作业或异想天开，提出新问题与方法创新型作业或异想天开，提出新问题与方法 请给出一个三角形是正三角形的条件请给出一个三角形是正三角形的条件并能用正弦定理证明。并能用正弦定理证明。Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.
