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Looking for the complete set of formulas of high school mathematical functions
Basic relations of trigonometric functions with the same angle

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