1、第2课时 简单的三角恒等变换,第五章 5.4 简单的三角恒等变换,NEIRONGSUOYIN,内容索引,题型分类 深度剖析,课时作业,题型分类 深度剖析,1,PART ONE,题型一 三角函数式的化简,自主演练,(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.,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,命题点2 给值求角,(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
2、某一三角函数值，再求角的范围确定角.,则(2sin 3cos )(sin cos )0，,2sin 3cos ，又sin2cos21，,题型三 三角恒等变换的应用,师生共研,(2)求f(x)的最小正周期及单调递增区间.,解 由cos 2xcos2xsin2x与sin 2x2sin xcos x，,所以f(x)的最小正周期是.,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.,思想方法,SIXIANGFANGFA,化归思想和整体代换思想在三角函数中的应用,讨论形如yasin xbcos x型函数的性质，一律化成y si
3、n(x)型的函数；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.,例 已知函数f(x)4tan xsincos. (1)求f(x)的定义域与最小正周期；,课时作业,2,PART TWO,基础保分练,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10
4、,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 cos4sin4(sin2cos2)(cos2sin2),1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,于是sin sin()sin cos()cos sin(),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,
5、12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,(1)求sin()的值；,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,技能提升练,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,(3,6,解析 在ABP中，由正弦定理得,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,拓展冲刺练,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,所以函数f(x)的最小正周期为.,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,
