·三角和的三角函数:
sin(α β γ)=sinα·cosβ·cosγ cosα·sinβ·cosγ cosα·cosβ·sinγ-sinα·sinβ·sinγ
cos(α β γ)=cosα·cosβ·cosγ-cosα·sinβ·sinγ-sinα·cosβ·sinγ-sinα·sinβ·cosγ
tan(α β γ)=(tanα tanβ tanγ-tanα·tanβ·tanγ)/(1-tanα·tanβ-tanβ·tanγ-tanγ·tanα)
·辅助角公式:
Asinα Bcosα=(A2 B2)^(1/2)sin(α t),其中
sint=B/(A2 B2)^(1/2)
cost=A/(A2 B2)^(1/2)
tant=B/A
Asinα-Bcosα=(A2 B2)^(1/2)cos(α-t),tant=A/B
·倍角公式:
sin(2α)=2sinα·cosα=2/(tanα cotα)
cos(2α)=cos2(α)-sin2(α)=2cos2(α)-1=1-2sin2(α)
tan(2α)=2tanα/[1-tan2(α)]
·三倍角公式:
sin(3α)=3sinα-4sin3(α)=4sinα·sin(60 α)sin(60-α)
cos(3α)=4cos3(α)-3cosα=4cosα·cos(60 α)cos(60-α)
tan(3α)=tana·tan(π/3 a)·tan(π/3-a)
·半角公式:
sin(α/2)=±√((1-cosα)/2)
cos(α/2)=±√((1 cosα)/2)
tan(α/2)=±√((1-cosα)/(1 cosα))=sinα/(1 cosα)=(1-cosα)/sinα
·降幂公式
sin2(α)=(1-cos(2α))/2=versin(2α)/2
cos2(α)=(1 cos(2α))/2=covers(2α)/2
tan2(α)=(1-cos(2α))/(1 cos(2α))
·万能公式: sinα=2tan(α/2)/[1 tan2(α/2)]
cosα=[1-tan2(α/2)]/[1 tan2(α/2)]
tanα=2tan(α/2)/[1-tan2(α/2)]