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)

Formulas of trigonometric functions of sum and difference of two angles.

General formula of trigonometric function

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 drop formula of trigonometric function

Sine, cosine and tangent formulas of double angles

Sine, cosine and tangent formulas of triple angle

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

Formula of product and difference 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

Coase α

sinβ=-[sin(α+β)-sin(α-β)]

2

1

Coase α

cosβ=-[cos(α+β)+cos(α-β)]

2

1

sinα

sinβ=—

-[cos(α+β)-cos(α-β)]

2