高考数学复习第四章三角函数解三角形4.5简单的三角恒等变换第二课时市赛课公开课一等奖省名师优质课获奖.pptx

剖析题型 提炼方法,实验解读,构建知识网络 强化答题语句,探究高考 明确考向,第,2,课时简单三角恒等变换,4.5,简单三角恒等变换,1/69,课时作业,题型分类深度剖析,内容索引,2/69,题型分类深度剖析,3/69,题型一三角函数式化简,自主演练,答案,解析,4sin,4/69,解析,答案,5/69,6/69,解析,答案,7/69,8/69,解析,答案,9/69,为第二象限角，,10/69,(1),三角函数式化简明遵照,“,三看,”,标准：一看角，二看名，三看式子结构与特征,.,(2),三角函数式化简明注意观察条件中角之间联络,(,和、差、倍、互余、互补等,),，寻找式子和三角函数公式之间共同点,.,思维升华,11/69,典例,(1)(,太原质检,)2sin 50,sin 10(1,tan,10),.,题型二三角函数求值,多维探究,命题点,1,给角求值与给值求值,答案,解析,12/69,13/69,答案,解析,14/69,15/69,16/69,答案,解析,17/69,cos,cos(,),cos(,)cos,sin(,)sin,18/69,命题点,2,给值求角,解析,答案,19/69,20/69,答案,解析,21/69,解析,tan,tan(,),22/69,23/69,引申探究,答案,解析,cos(,),cos,cos,sin,sin,24/69,(1),给角求值与给值求值问题关键在,“,变角,”,，经过角之间联络寻找转化方法,.,(2),给值求角问题：先求角某一三角函数值，再求角范围确定角,.,思维升华,25/69,答案,解析,26/69,则,(2sin,3cos,)(sin,cos,),0,，,2sin,3cos,，又,sin,2,cos,2,1,，,27/69,解析,4,答案,28/69,解析,答案,29/69,于是,sin,sin,(,),sin,cos(,),cos,sin(,),30/69,典例,(,浙江,),已知函数,f,(,x,),sin,2,x,cos,2,x,2 sin,x,cos,x,(,x,R,).,(1),求,值；,题型三三角恒等变换应用,师生共研,解答,31/69,解,由,cos 2,x,cos,2,x,sin,2,x,与,sin 2,x,2sin,x,cos,x,，得,所以,f,(,x,),最小正周期是,.,由正弦函数性质，得,(2),求,f,(,x,),最小正周期及单调递增区间,.,解答,32/69,三角恒等变换应用策略,(1),进行三角恒等变换要抓住：变角、变函数名称、变结构，尤其是角之间关系；注意公式逆用和变形使用,.,(2),把形如,y,a,sin,x,b,cos,x,化为,y,sin(,x,),，可深入研究函数周期性、单调性、最值与对称性,.,思维升华,33/69,答案,解析,跟踪训练,(1),函数,f,(,x,),sin(,x,),2sin,cos,x,最大值为,.,1,解析,因为,f,(,x,),sin(,x,),2sin,cos,x,sin,x,cos,cos,x,sin,sin(,x,),，,又,1,sin(,x,),1,，,所以,f,(,x,),最大值为,1.,34/69,解析,答案,35/69,化归思想和整体代换思想在三角函数中应用,思想方法,思想方法指导,思想方法指导,(1),讨论形如,y,a,sin,x,b,cos,x,型函数性质，一律化成,y,sin(,x,),型函数,.,(2),研究,y,A,sin(,x,),型函数最值、单调性，可将,x,视为一个整体，换元后结合,y,sin,x,图象处理,.,规范解答,36/69,规范解答,37/69,38/69,39/69,课时作业,40/69,基础保,分练,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,解析,答案,41/69,答案,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,解析,42/69,答案,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,解析,43/69,解析,答案,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,44/69,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,即,sin,cos,cos,cos,sin,，,45/69,解析,答案,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,46/69,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,47/69,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,解析,答案,48/69,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,解析,f,(,x,),5cos,x,12sin,x,49/69,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,解析,答案,50/69,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,解析,答案,51/69,tan,0,且,tan,0,，,即,0,，结合,tan(,),1,，,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,52/69,解析,答案,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,53/69,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,解析,cos,4,sin,4,(sin,2,cos,2,)(cos,2,sin,2,),2,(0,，,),，,54/69,解析,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,答案,55/69,解答,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,56/69,12.,已知函数,f,(,x,),cos,2,x,sin,x,cos,x,，,x,R,.,(1),求,值；,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,解答,57/69,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,解答,58/69,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,59/69,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,60/69,技能提升练,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,解析,答案,61/69,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,62/69,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,63/69,解析,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,答案,14.,在斜,ABC,中，,sin,A,cos,B,cos,C,，且,tan,B,tan,C,1,，,则角,A,值为,.,64/69,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,65/69,拓展冲刺练,解析,答案,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,66/69,16.(,泉州模拟,),已知角,顶点在坐标原点，始边与,x,轴正半轴重合，终边经过点,P,(,3,，,).,(1),求,sin 2,tan,值；,解答,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,sin 2,tan,2sin,cos,tan,67/69,解答,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,68/69,解,f,(,x,),cos(,x,)cos,sin(,x,)sin,cos,x,，,x,R,，,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,69/69,