1、4.5三角恒等变形,第四章三角函数、解三角形,基础知识自主学习,课时作业,题型分类深度剖析,内容索引,基础知识自主学习,1.两角和与差的余弦、正弦、正切公式cos()cos cos sin sin (C()cos() (C()sin() (S()sin() (S(),知识梳理,cos cos sin sin ,sin cos cos sin ,sin cos cos sin ,2.二倍角公式sin 2 ；cos 2 ；tan 2 .,2sin cos ,cos2sin2,2cos21,12sin2,2.升幂公式：1cos 22cos2，1cos 22sin2.,【知识拓展】,题组一思考辨析1.
2、判断下列结论是否正确(请在括号中打“”或“”)(1)存在实数，使等式sin()sin sin 成立.(),基础自测,1,2,3,4,5,6,7,(3)y3sin x4cos x的最大值是7.()(4)公式tan() 可以变形为tan tan tan()(1tan tan )，且对任意角，都成立.(),题组二教材改编,1,2,4,5,6,答案,3,解析,7,解析是第三象限角，,1,2,4,5,6,解析,3.sin 347cos 148sin 77cos 58 .,解析sin 347cos 148sin 77cos 58sin(27077)cos(9058)sin 77cos 58(cos 77)
3、(sin 58)sin 77cos 58sin 58cos 77cos 58sin 77,3,7,答案,4.tan 20tan 40 tan 20tan 40 .,解析,1,2,4,5,6,3,答案,7,tan 20tan 40tan 60(1tan 20tan 40),题组三易错自纠5.化简： .,解析,1,2,4,5,6,3,答案,7,6.(2018昆明模拟)若tan ，tan() ，则tan .,解析,1,2,4,5,6,3,7,答案,解析,1,2,4,5,6,3,7,答案,1,2,4,5,6,3,7,1,2,4,5,6,3,7,题型分类深度剖析,第1课时两角和与差的正弦、余弦和正切公式
4、,题型一和差公式的直接应用,自主演练,答案,解析,解析,答案,解析,答案,(1)使用两角和与差的三角函数公式，首先要记住公式的结构特征.(2)使用公式求值，应先求出相关角的函数值，再代入公式求值.,题型二和差公式的灵活应用,多维探究,命题点1角的变换,答案,解析,于是cos cos()cos()cos sin()sin ,(2)(2017泰安模拟)已知cos(75) ，则cos(302)的值为 .,答案,解析,命题点2三角函数式的变换,解答,解答,解答,(1)解决三角函数的求值问题的关键是把“所求角”用“已知角”表示.当“已知角”有两个时，“所求角”一般表示为两个“已知角”的和或差的形式；当“
5、已知角”有一个时，此时应着眼于“所求角”与“已知角”的和或差的关系.,跟踪训练 (1)(2017豫北名校联考)计算： .(用数字作答),答案,解析,答案,解析,用联系的观点进行三角变形,思想方法,思想方法指导,2,思想方法指导 三角变形的关键是找到条件和结论中的角和式子结构之间的联系.变形中可以通过适当地拆角、凑角或对式子整体变形达到目的.,答案,解析,(2)原式1tan 17tan 28tan 17 tan 281tan 45(1tan 17 tan 28)tan 17 tan 28112.,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,
6、解析,答案,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,答案,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,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asin 40cos 127cos 40sin 127sin(40127)sin 167sin 13，,sin(5645)sin 11，,sin 13sin
7、12sin 11，acb.,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,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,答案,解析,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,1,2,3,4,5,6,7,8,9,10,1
8、1,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,6tan 61tan (tan 1)，,解析,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,答案,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,答案,解析,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,答案,解析,解析依题意可将已知条件变形为,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,技能提升练,答案,1,2,3,4,5,6,7,8,9,10,11,12
9、,13,14,15,16,解析,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,15.(2017武汉调研)设，0，且满足sin cos cos sin 1，则sin(2)sin(2)的取值范围为 .,拓展冲刺练,解析,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,答案,1,1,解析由sin cos cos sin 1，得sin()1，,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,16.(2017合肥模拟)已知函数f(x)(2cos2x1)sin 2x cos 4x.(1)求f(x)的最小正周期及递减区间；,解答,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,解答,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,本课结束,
