第1个回答 2020-05-28
三角函数转换公式
1、诱导公式:sin(-α)
=
-sinα;cos(-α)
=
cosα;sin(π/2-α)
=
cosα;cos(π/2-α)
=
sinα; sin(π/2+α)
=
cosα;cos(π/2+α)
=
-sinα;sin(π-α)
=
sinα;cos(π-α)
=
-cosα; sin(π+α)
=
-sinα;cos(π+α)
=
-cosα;tana=
sina/cosa;tan(π/2+α)=-cotα;tan(π/2-α)=cotα;tan(π-α)=-tanα;tan(π+α)=tanα
2、两角和差公式:
sin(ab)
=
sinacosbcosasinb
cos(ab)
=
cosacosbsinasinb
tan(ab)
=
(tanatanb)/(1tanatanb)
cot(ab)
=
(cotacotb1)/(cotbcota)
3、倍角公式 sin2a=2sina•cosa
cos2a=cosa2-sina2=1-2sina2=2cosa2-1
tan2a=2tana/(1-tana2)=2cota/(cota2-1)4、半角公式 tan(a/2)=(1-cosa)/sina=sina/(1+cosa);
cot(a/2)=sina/(1-cosa)=(1+cosa)/sina.
sin^2(a/2)=(1-cos(a))/2
cos^2(a/2)=(1+cos(a))/2
tan(a/2)=(1-cos(a))/sin(a)=sin(a)/(1+cos(a))
5、和差化积 sinθ+sinφ
=
2
sin[(θ+φ)/2]
cos[(θ-φ)/2]
sinθ-sinφ
=
2
cos[(θ+φ)/2]
sin[(θ-φ)/2]
cosθ+cosφ
=
2
cos[(θ+φ)/2]
cos[(θ-φ)/2]
cosθ-cosφ
=
-2
sin[(θ+φ)/2]
sin[(θ-φ)/2]
tana+tanb=sin(a+b)/cosacosb=tan(a+b)(1-tanatanb)
tana-tanb=sin(a-b)/cosacosb=tan(a-b)(1+tanatanb)
6、积化和差 sinαsinβ
=
-1/2*[cos(α-β)-cos(α+β)]
cosαcosβ
=
1/2*[cos(α+β)+cos(α-β)]
sinαcosβ
=
1/2*[sin(α+β)+sin(α-β)]
cosαsinβ
=
1/2*[sin(α+β)-sin(α-β)]万能公式