1、第2课时简单的三角恒等变换,4.5简单的三角恒等变换,课时作业,题型分类深度剖析,内容索引,题型分类深度剖析,题型一三角函数式的化简,自主演练,答案,解析,4sin ,解析,答案,解析,答案,解析,答案,为第二象限角，,(1)三角函数式的化简要遵循“三看”原则：一看角，二看名，三看式子结构与特征.(2)三角函数式的化简要注意观察条件中角之间的联系(和、差、倍、互余、互补等)，寻找式子和三角函数公式之间的共同点.,典例 (1)(2018太原质检)2sin 50sin 10(1 tan 10) .,题型二三角函数的求值,多维探究,命题点1给角求值与给值求值,答案,解析,答案,解析,答案,解析,co
2、s cos()cos()cos sin()sin ,命题点2给值求角,解析,答案,答案,解析,解析tan tan(),答案,解析,cos()cos cos sin sin ,(1)给角求值与给值求值问题的关键在“变角”，通过角之间的联系寻找转化方法.(2)给值求角问题：先求角的某一三角函数值，再求角的范围确定角.,答案,解析,则(2sin 3cos )(sin cos )0，,2sin 3cos ，又sin2cos21，,解析,4,答案,解析,答案,于是sin sin()sin cos()cos sin(),典例 (2017浙江)已知函数f(x)sin2xcos2x2 sin xcos x(x
3、R).(1)求 的值；,题型三三角恒等变换的应用,师生共研,解答,解由cos 2xcos2xsin2x与sin 2x2sin xcos x，得,所以f(x)的最小正周期是.由正弦函数的性质，得,(2)求f(x)的最小正周期及单调递增区间.,解答,三角恒等变换的应用策略(1)进行三角恒等变换要抓住：变角、变函数名称、变结构，尤其是角之间的关系；注意公式的逆用和变形使用.(2)把形如yasin xbcos x化为y sin(x)，可进一步研究函数的周期性、单调性、最值与对称性.,答案,解析,跟踪训练(1)函数f(x)sin(x)2sin cos x的最大值为 .,1,解析因为f(x)sin(x)2
4、sin cos xsin xcos cos xsin sin(x)，又1sin(x)1，所以f(x)的最大值为1.,解析,答案,化归思想和整体代换思想在三角函数中的应用,思想方法,思想方法指导,思想方法指导(1)讨论形如yasin xbcos x型函数的性质，一律化成y sin(x)型的函数.(2)研究yAsin(x)型函数的最值、单调性，可将x视为一个整体，换元后结合ysin x的图象解决.,规范解答,规范解答,课时作业,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,答案,1,2,3,4,5,6,7,8,9,10,11,12,13,14
5、,15,16,解析,答案,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,解析,解析,答案,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,即sin cos cos cos sin ，,解析,答案,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,解析,答案,1,2,3,4,5
6、,6,7,8,9,10,11,12,13,14,15,16,解析f(x)5cos x12sin x,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,解析,答案,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,解析,答案,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,解析,答案,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,解析cos4sin4(
7、sin2cos2)(cos2sin2),2(0，)，,解析,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,答案,解答,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,12.已知函数f(x)cos2xsin xcos x，xR.(1)求 的值；,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,解答,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,解答,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,
8、12,13,14,15,16,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,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,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 Bcos C，且tan Btan C1 ，则角A的值为 .,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,拓展冲刺练,解析,答案,1,2,3,4,5,6,7,8,9,10,11,12,13,
