Reciprocal relation: quotient relation: square relation:
tanα cotα= 1
sinα cscα= 1
cosαsecα= 1 sinα/cosα= tanα= secα/CSCα
cosα/sinα= cotα= CSCα/secαsin 2α+cos 2α= 1
1+tan2α=sec2α
1+cot2α=csc2α
Inductive formula
Sine (-α) =-Sine α
cos(-α)=cosα tan(-α)=-tanα
Kurt (-α) =-Kurt α
sin(π/2-α)=cosα
cos(π/2-α)=sinα
tan(π/2-α)=cotα
cot(π/2-α)=tanα
sin(π/2+α)=cosα
cos(π/2+α)=-sinα
tan(π/2+α)=-cotα
cot(π/2+α)=-tanα
Sine (π-α) = Sine α
cos(π-α)=-cosα
tan(π-α)=-tanα
cot(π-α)=-coα
Sine (π+α) =-Sine α
cos(π+α)=-cosα
tan(π+α)=tanα
cot(π+α)=cotα
sin(3π/2-α)=-cosα
cos(3π/2-α)=-sinα
tan(3π/2-α)=cotα
cot(3π/2-α)=tanα
sin(3π/2+α)=-cosα
cos(3π/2+α)=sinα
tan(3π/2+α)=-cotα
cot(3π/2+α)=-tanα
Sine (2π-α)=- Sine α
cos(2π-α)=cosα
tan(2π-α)=-tanα
Kurt (2π-α)=- Kurt α
sin(2kπ+α)=sinα
cos(2kπ+α)=cosα
tan(2kπ+α)=tanα
cot(2kπ+α)=cotα
(where k∈Z)
General formula for sum and difference of formulas of trigonometric functions's two angles
sin(α+β)=sinαcosβ+cosαsinβ
sin(α-β)=sinαcosβ-cosαsinβ
cos(α+β)=cosαcosβ-sinαsinβ
cos(α-β)=cosαcosβ+sinαsinβ
tanα+tanβ
tan(α+β)=———
1-tanα tanβ
tanα-tanβ
tan(α-β)=———
1+tanα tanβ
2 tons (α/2)
sinα=————
1+tan2(α/2)
1-tan2(α/2)
cosα=————
1+tan2(α/2)
2 tons (α/2)
tanα=————
1-tan2(α/2)
Sine, cosine and tangent formulas of half angle; Power reduction formula of trigonometric function
Sine, cosine and tangent formulas of double angles Sine, cosine and tangent formulas of triangle
sin2α=2sinαcosα
cos 2α= cos 2α-sin 2α= 2 cos 2α- 1 = 1-2 sin 2α
2tanα
tan2α=———
1-tan2α
sin3α=3sinα-4sin3α
cos3α=4cos3α-3cosα
3tanα-tan3α
tan3α=————
1-3tan2α
Sum and difference product formula of trigonometric function
α+β α-β
sinα+sinβ= 2 sin—-cos——
2 2
α+β α-β
sinα-sinβ= 2cos—-sin——
2 2
α+β α-β
cosα+cosβ= 2cos—-cos——
2 2
α+β α-β
cosα-cosβ=-2 sin—-sin——
2 2 1
sinα cosβ=-[sin(α+β)+sin(α-β)]
2
1
cosα sinβ=-[sin(α+β)-sin(α-β)]
2
1
cosα cosβ=-[cos(α+β)+cos(α-β)]
2
1
sinαsinβ=-[cos(α+β)-cos(α-β)]
2
Convert asinα bcosα into trigonometric function form of angle (formulas of trigonometric functions of auxiliary angle