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1、三角函数的诱导公式【精品-】诱导公式（一）实质：终边相同，三角函数值相等用途：“大”角化“小”角回忆:单位圆中 三角函数的定义？P(x,y)xyo因为所以诱导公式的变形诱导公式（四）P(x,y)yx01-1-11P′(-x,y)由对称性及单位圆上三角函数的定义可得：乘胜追击诱导公式（五）P′(y,x)P(x,y)yx01-1-11两角互余，正弦等于余弦诱导公式（六）诱导公式的变形诱导公式的变形公式回顾和总结共同点：函数名不变,符号与前面值的正负一至.共同点：函数名改变,符号与前面值的正负一至.※
2、记忆方法：奇变偶不变，符号看象限．说明：牛刀小试挖掘角的相互关系，寻求诱导公式的应用互余关系变式练习：牛刀小试挖掘角的相互关系，寻求诱导公式的应用互补关系牛刀小试牛刀小试牛刀小试牛刀小试牛刀小试能力提升规律探索001-1原理解释巩固练习1利用公式求下列三角函数值.2.已知,α是第四象限角,则的值是_______.3化简5.已知,求4.求值:6.已知,求的值.9.已知,求8.已知,求的值.7.已知,且,求的值.12.已知,α为第三象限角,求的值.11.已知,求的值.利用诱导公式负转正，大变小2tan
3、(-)=-tan成立的条件是（）A为不等于/2的任意角B锐角CRDk+/2,kZ且RD例题与练习例3已知sin(x+/6)=1/4,求sin(7/+x)+sin2(5/6-x)的值。例题与练习已知角的终边上的一点P(3a,4a)(a<0)则cos(5400-)的值是。3/52cos(-8/3)+cos(+13/3)=.032sin2(11/4)+tan2(33/4)·cot(3/4)=.0已知cos(750+)=1/3,求cos(1050-)
4、+cos(2850-)0例题与练习例4化简练习1求sin(2n+2/3)·cos(n+4/3)的值(nZ)2化简cos[(4n+1)/4+x]+cos[(4n-1)/4-x]当n为奇数时，原式=-2cos(/4+x)当n为偶数时，原式=2cos(/4+x)当n为偶数时，当n为奇数时，练习1sin(7/3)=,2sin(8/3)=,3sin(10/3)=,4sin(11/3)=,cos(7/3)=,2cos(8/3)=,3cos(10/3)=,4cos(11/3)
5、=,1tan(7/3)=,tan(8/3)=,tan(10/3)=,4tan(11/3)=,onljhfdb97531+-(&$#YWUSQOMLJHFDBzxvtrpomkigeca86420+)*%!ZXVTRPNMKIGECAywusqpnljhfdb975310-(&$#YWUSQONLJHFDBzxvtrqomkigeca86421+)*%!ZXVTRPOMKIGECAywusrpnljhfdb975320-(&$#YWUSQPNLJHFDBzxvtsqomkigeca86431
6、+)*%!ZXVTRQOMKIGECAywutrpnljhfdb975420-(&$#YWUSRPNLJHFDBzxvusqomkigeca86531+)*%!ZXVTSQOMKIGECAywvtrpnljhfdb986420-(&$#YWUTRPNLJHFDBzxwusqomkigeca97531+)*%!ZXVUSQOMKIGECAyxvtrpnljhfdba86420-(&$#YWVTRPNLJHFDBzywusqomkigecb97531+)*%!ZXWUSQOMKIGECAzxvtrpn
7、ljhfdca86420-(&$#YXVTRPNLJHFDBAywusqomkigedb97531+)*%!ZYWUSQOMKIGECBzxvtrpnljhfeca86420-(&$#ZXVTRPNLJHFDCAywusqomkigfdb97531+)*%!#YWUSQOMKIGEDBzxvtrpnljhgeca86420-(&$!ZXVTRPNLJHFECAywusqomkihfdb97531+)*%$#YWUSQOMKIGFDBzxvtrpnljigeca86420-(*%!ZXVTRPNLJ
8、HGECAywusqomkjhfdb97531+)(&$#YWUSQOMKIHFDBzxvtrpnlkigeca86420-)*%!ZXVTRPNLJIGECAywusqomljhfdb97531+-(&$#YWUSQOMKJHFDBzxvtrpnmkigeca86420+)*%!ZXVTRPNLKIGECAywusqonljhfdb975310-(&$#YWUSQOMLJHFDBzxvtrpomkigeca86421+)*%!ZXVTRPNMKIGECAywusqpnljhfdb
