高考数学复习第四章三角函数解三角形4.5三角恒等变形第一课时两角和与差的正弦余弦和正切公式市赛课公开.pptx

,4.5,三角恒等变形,1/49,基础知识自主学习,课时作业,题型分类深度剖析,内容索引,2/49,基础知识自主学习,3/49,tan(,),.(T,),tan(,),，,(T,),cos(,),cos,cos,sin,sin,，,(C,),cos(,),，,(C,),sin(,),，,(S,),sin(,),，,(S,),1.,两角和与差余弦、正弦、正切公式,知识梳理,cos,cos,sin,sin,sin,cos,cos,sin,sin,cos,cos,sin,4/49,sin 2,；,(S,2,),cos 2,；,(C,2,),2.,二倍角公式,tan 2,.(T,2,),2sin,cos,cos,2,sin,2,2cos,2,1,1,2sin,2,5/49,知识拓展,2.,升幂公式：,1,cos 2,2cos,2,，,1,cos 2,2sin,2,.,6/49,判断以下结论是否正确,(,请在括号中打,“”,或,“”,),(1),存在实数,，,，使等式,sin(,),sin,sin,成立,.(,),(2),在锐角,ABC,中，,sin,A,sin,B,和,cos,A,cos,B,大小不确定,.(,),(3),若,45,，则,tan,tan,1,tan,tan,.(,),(4),对任意角,都有,1,sin,(sin,cos ),2,.(,),(5),y,3sin,x,4cos,x,最大值是,7.(,),(6),在非直角三角形中，,tan,A,tan,B,tan,C,tan,A,tan,B,tan,C,.(,),思索辨析,7/49,1.(,教材改编,)sin 18cos 27,cos 18sin 27,值是,考点自测,答案,解析,sin 18cos 27,cos 18sin 27,sin(18,27),sin 45,.,8/49,答案,解析,9/49,答案,解析,10/49,答案,解析,tan 20,tan 40,tan 60(1,tan 20tan 40),11/49,答案,解析,12/49,题型分类深度剖析,第,1,课时两角和与差正弦、余弦和正切公式,13/49,题型一和差公式直接应用,答案,解析,14/49,(2),在,ABC,中，若,tan,A,tan,B,tan,A,tan,B,1,，则,cos,C,值为,答案,解析,由,tan,A,tan,B,tan,A,tan,B,1,，,15/49,思维升华,(1),使用两角和与差三角函数公式，首先要记住公式结构特征,.,(2),使用公式求值，应先求出相关角函数值，再代入公式求值,.,16/49,跟踪训练,1,(1)(,全国丙卷,),若,tan,，则,cos,2,2sin 2,等于,答案,解析,17/49,答案,解析,18/49,题型二和差公式综合应用,命题点,1,角变换,答案,解析,19/49,又,，,均为锐角，所以,0,cos(,).,于是,cos,cos,(,),cos(,)cos,sin(,)sin,20/49,答案,解析,21/49,命题点,2,三角函数式变形,解答,22/49,23/49,解答,24/49,引申探究,解答,25/49,思维升华,(1),处理三角函数求值问题关键是把,“,所求角,”,用,“,已知角,”,表示,.,当,“,已知角,”,有两个时，,“,所求角,”,普通表示为两个,“,已知角,”,和或差形式；,当,“,已知角,”,有一个时，此时应着眼于,“,所求角,”,与,“,已知角,”,和或差关系，然后应用诱导公式把,“,所求角,”,变成,“,已知角,”.,26/49,答案,解析,27/49,答案,解析,A.cos,2,B.sin,2,C.cos 2,D.,cos 2,28/49,答案,解析,1,29/49,A.1 B.2C.3 D.4,答案,解析,利用联络观点进行角变换,思想与方法系列,8,思想方法指导,30/49,31/49,32/49,课时作业,33/49,1.(,课标全国,)sin 20cos 10,cos 160sin 10,等于,1,2,3,4,5,6,7,8,9,10,11,12,13,答案,解析,sin 20cos 10,cos 160sin 10,sin 20cos 10,cos 20sin 10,sin(20,10),sin 30,.,34/49,1,2,3,4,5,6,7,8,9,10,11,12,13,答案,解析,35/49,答案,解析,1,2,3,4,5,6,7,8,9,10,11,12,13,36/49,1,2,3,4,5,6,7,8,9,10,11,12,13,答案,解析,37/49,答案,解析,1,2,3,4,5,6,7,8,9,10,11,12,13,38/49,答案,解析,1,2,3,4,5,6,7,8,9,10,11,12,13,39/49,1,2,3,4,5,6,7,8,9,10,11,12,13,答案,解析,40/49,答案,解析,sin 2,2cos,2,sin 2,cos 2,1,1,2,3,4,5,6,7,8,9,10,11,12,13,41/49,答案,解析,依题意可将已知条件变形为,1,2,3,4,5,6,7,8,9,10,11,12,13,42/49,答案,解析,1,2,3,4,5,6,7,8,9,10,11,12,13,43/49,1,2,3,4,5,6,7,8,9,10,11,12,13,解答,44/49,又,sin,2,cos,2,1,，,5sin,2,1,，,1,2,3,4,5,6,7,8,9,10,11,12,13,45/49,(1),求,cos,值；,1,2,3,4,5,6,7,8,9,10,11,12,13,解答,46/49,解答,cos,cos,(,),cos,cos(,),sin,sin(,),1,2,3,4,5,6,7,8,9,10,11,12,13,47/49,(1),求,sin 2,值；,解答,1,2,3,4,5,6,7,8,9,10,11,12,13,48/49,解答,1,2,3,4,5,6,7,8,9,10,11,12,13,49/49,