常用的三角函数公式大全

三角函数公式两角和公式sin(A+B)=sinAcosB+cosAsinBsin(A-B)=sinAcosB-cosAsinBcos(A+B)=cosAcosB-sinAsinBcos(A-B)=cosAcosB+sinAsinBtan(A+B)=tanAtanB-1tanBtanAtan(A-B)=tanAtanB1tanBtanAcot(A+B)=cotAcotB1-cotAcotBcot(A-B)=cotAcotB1cotAcotB倍角公式tan2A=Atan12tanA2Sin2A=2SinA•CosACos2A=Cos2A-Sin2A=2Cos2A-1=1-2sin2A三倍角公式sin3A=3sinA-4(sinA)3cos3A=4(cosA)3-3cosAtan3a=tana·tan(3+a)·tan(3-a)半角公式sin(2A)=2cos1Acos(2A)=2cos1Atan(2A)=AAcos1cos1cot(2A)=AAcos1cos1tan(2A)=AAsincos1=AAcos1sin和差化积sina+sinb=2sin2bacos2basina-sinb=2cos2basin2bacosa+cosb=2cos2bacos2bacosa-cosb=-2sin2basin2batana+tanb=babacoscos)sin(积化和差sinasinb=-21[cos(a+b)-cos(a-b)]cosacosb=21[cos(a+b)+cos(a-b)]sinacosb=21[sin(a+b)+sin(a-b)]cosasinb=21[sin(a+b)-sin(a-b)]万能公式sina=2)2(tan12tan2aacosa=22)2(tan1)2(tan1aatana=2)2(tan12tan2aa其它公式a•sina+b•cosa=)b(a22×sin(a+c)[其中tanc=ab]a•sin(a)-b•cos(a)=)b(a22×cos(a-c)[其中tan(c)=ba]1+sin(a)=(sin2a+cos2a)21-sin(a)=(sin2a-cos2a)2其他非重点三角函数csc(a)=asin1sec(a)=acos1双曲函数sh(a)=2e-e-aach(a)=2ee-aath(a)=)()(achashch2A-sh2A=1sh2A=2shAchAch2A=ch2A+sh2A设α为任意角，2n+α的三角函数值与α的三角函数值之间的关系：假设α为锐角时，先计算2n+α的值，再确定符号，如果n为偶数，则三角函数不变，否则转换函数，同时去掉2n，例如sin（2n＋α）cos（2n＋α）tan（2n＋α）cot（2n＋α）