三角函数常用公式(表格)

1、精品资料欢迎下载同角三角函数的基本关系式诱导公式sin(a)=sinacos(a) =cosatan(a )=tanacot(a )=cotasin(n/2a) =cosasin(n a) =Sinasin(3n/2-a)=cosasin(2n a)=sinacos(n/2a ) =Sinacos(n a) =cosacos(3n/ a )=sinacos(2n a)=cosatan(n/2a ) =cotatan(n a ) =tanatan(3n/2-a)=cotatan(2n a )= =tanacot(n/2a ) =tanacot(n a ) =cotacot(3n/2-a )=ta

2、nacot(2n a)=cotasin(n/2+a) =cosasin(n+ a) =Sinasin(3n/2+ a)=cosasin(2kn+ a )=sinacos(n/2+ a ) =Sinacos(n+ a) =cosacos(3n/2+ a )=sinacos(2kn+ a)=cosatan(n/2+a ) =cotatan(n+ a ) =tanatan(3n/2+ a)=cotatan(2kn + a)=tanacot(n/2+a ) =tanacot(n+a ) =cotacot(3n/2+ a )=tanacot(2kn+ a)=cota(其中kZ)tana+tan3tan(

3、a+ 3)=atan31tantanatan3tan(a 3)=1+tanatan3万能公式2tan(a/2)sina=-21+tan (a/2)21tan (a/2)COSa=-21+tan (a/2)2tan(a/2)tana=-21tan (a/2)tanacot 1asina+cosa=1sina/cos =dtana=seca/csca22sinaCSC1a1+tana=secasec1cosa/sin=acota=csca/seca丄.22cosaa1+cota=csca倒数关系：商的关系:平方关系:2 2三角函数的降幕公式 _+.Sin2飞飞r - COS Ct2c号士N1 +

4、cosa2tan|=fl -cosa _cosa _ since1 COSQsina1十cos ex半角的正弦、余弦和正切公式.乜乜1亠cos 2心sin a =-221 + COS 2ftcos 0 =-2sin(a+ 3 )=sinaCOS+COSasin3sin(a 3)=sinacos3cosasin3cos(a+3 )=cosacossinasin3cos(a 3)=cosacos+sinasin3两角和与差的三角函数公式精品资料欢迎下载精品资料欢迎下载和差化积公式a+ 3a 3sin+sin=2si n -cos2 2a+ 3a 3sin(sin=2cos -sin2 2a+ 3a

5、 3cosa+cos3=2cos -COS2 2a+ 3a 3cosacos3=2sin -sin2 2化asinabcosa为一个角的一个三角函数的形式（辅助角的三角函数公式）ar ansin JAI二倍角的正弦、余弦和正切公式sin2a=2sinaCOSa三倍角的正弦、余弦和正切公式cos22 . 2 2oc=cosa sina=2cosa1=12sinsin3 a= 3sina-4sincos3a=4cos3小a3cos2tanatan2oc=-21tana3tanatan3atan3a=-13ta na积化和差公式1sina co&3n( a+ 3) +sin( a 3)21cosa S=-3n( a+ 3) sin( a 3)21cosa co=-3os( a+ 3 ) +COS( a