Trigonometric Functions

Pathogorean Identities

Cos²θ+Sin²θ=1

Sec²θ=1+Tan²θ

Csc²θ=1+Cot²θ

Quotient Identities

Tanθ= Cosθ/Sinθ

Cotθ=Sinθ/Cosθ

Double Angle Identities

Sin(2θ)=2sinθcosθ

Cos(2θ)=

cos²θ-sin²θ

1-Sin²θ

2Cos²θ-1

Tan(2θ)=2tanθ
1-tan²θ

Reciprocal Identities

Cscθ=1/Sinθ

Secθ=1/Cosθ

Cotθ=1/Tanθ

Half Angle Identities

Sin(θ/2)=±√(1/2)(1-cosθ)

Cos(θ/2)=±√(1/2)(1+cosθ)

Tan(2/θ)=sin(2/θ)
cos(2/θ)

SumIdentities

Tan(α±ß)=tanα±tanß
1±tanαtanß

Cos(α±ß)=cosαcosß±sinαsinß

Sin(α±ß)=sinαcosß±cosαsinß

Even and Odd

Even
Cos
Sec

Odd
Sin
Csc
Tan
Cot

Sinθ=Opposite/Hypotenuse

CSCθ=Hypotenuse/Opposite

Sin^-1

Domain:
[-1,1]

Range:
[-π/2,π/2]

Cosθ=Adjacent/Hypotensue

Secθ=Hypotensue/ Adjacent

Cos^-1

Domain
[-1,1]

Range
[0,π]

Tanθ=Opposite/Adjacent

Cotθ=Adjacent/Opposite

Tan^-1

Domain:
(-∞,∞)

Range
(-π/2,π/2)