高中三角函数公式大全

高中三角函数公式大全

三角函数公式

两角和公式

sin(A+B) = sinAcosB+cosAsinB sin(A-B) = sinAcosB-cosAsinB cos(A+B) = cosAcosB-sinAsinB cos(A-B) = cosAcosB+sinAsinB

tanAtanBtan(A+B) =

1-tanAtanBtanAtanBtan(A-B) = 1tanAtanBcotAcotB-1cot(A+B) = cotBcotAcotAcotB1cot(A-B) = cotBcotA倍角公式 2tanAtan2A = 21tanASin2A=2SinA•CosA Cos2A = Cos2A-Sin2A=2Cos2A-1=1-2sin2A 半角公式 sin(A1cosA)= 22A1cosA)= 22A1cosA)= 21cosAA1cosA)= 21cosAcos(tan(cot(tan(

A1cosAsinA)==

sinA1cosA2和差化积

ababsina+sinb=2sincos

22ababsina-sinb=2cossin

22ababcosa+cosb = 2coscos

22

ababsin 22sin(ab)tana+tanb=

cosacosb积化和差

1sinasinb = -[cos(a+b)-cos(a-b)]

21cosacosb = [cos(a+b)+cos(a-b)]

21sinacosb = [sin(a+b)+sin(a-b)]

21cosasinb = [sin(a+b)-sin(a-b)] 2诱导公式 sin(-a) = -sina cos(-a) = cosa cosa-cosb = -2sin

-a) = cosa 2cos(-a) = sina 2sin(+a) = cosa 2cos(+a) = -sina 2sin(π-a) = sina cos(π-a) = -cosa sin(π+a) = -sina cos(π+a) = -cosa sinatgA=tanA = cosa万能公式 a2tan2 sina=a1(tan)22a1(tan)22 cosa=

a1(tan)22a2tan2 tana=

a1(tan)22sin(