高一三角函数公式大全

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tanBtanAtanB tan(A-B) =

1-tanAtanB1tanAtanBcotAcotB-1cotAcotB1cot(A+B) = cot(A-B) =

cotBcotAcotBcotA

tan(A+B) =倍角公式 tan2A =

2tanA Sin2A=2SinA•CosA

1tan2ACos2A = Cos2A-Sin2A=2Cos2A-1=1-2sin2A

三倍角公式

sin3A = 3sinA-4(sinA)3 cos3A = 4(cosA)3-3cosA tan3a = tana·tan(

半角公式 sin(

1cosA1cosAAA)= cos()=

22221cosA1cosAAA)= cot()=

1cosA1cosA22+a)·tan(-a) 33tan(tan(

A1cosAsinA)==

sinA1cosA2和差化积

ababababcos sina-sinb=2cossin 2222ababababcosa+cosb = 2coscos cosa-cosb = -2sinsin

2222sin(ab)tana+tanb=

cosacosb

sina+sinb=2sin

积化和差 sinasinb = -1[cos(a+b)-cos(a-b)] cosacosb = 21[cos(a+b)+cos(a-b)] 211sinacosb = [sin(a+b)+sin(a-b)] cosasinb = [sin(a+b)-sin(a-b)]

2

诱导公式

sin(-a) = -sina cos(-a) = cosasin(

2-a) = cosa cos(sin(2+a) = cosa cos(sin(π-a) = sina sin(π+a) = -sina tgA=tanA =sinacosa

万能公式

2tanasina=

2 cosa=1(tana)22

2

2-a) = sina 2+a) = -sina

cos(π-a) = -cosa cos(π+a) = -cosa 1(tanaa2)22tan tana=2 1(tana)21(tana)222