Trigonometric Identities

Even/Odd Identities

Sin(-θ)=-sin(θ) Cos(-θ)=cos(θ) Tan(-θ)=-tan(θ) Csc(-θ)=-csc(θ) Sec(-θ)=sec(θ) Cot(-θ)=-Cot(θ)

Double Angle Identities

Sin(2θ) = 2SinθCosθ Cos(2θ) = Cos^2θ - Sin^2θ Cos(2θ) = 2Cos^2θ - 1 Cos(2θ) = 1 - 2Sin^2θ Tan(2θ) = (2Tanθ) / (1 - Tan^2θ)

Pythagorean Identities

Sin^2θ+Cos^2θ=1 1+cot^2θ=csc^2θ 1+tan^2θ=sec^2θ

Reduction Identities

Sin^2θ=1-cos^2θ/2 Cos^2θ=1+cos^2θ/2 Tan^2θ=1-cos^2θ/1+cos^2θ

Cofunction Identities

Sinθ=cos(π/2-θ) Cosθ=sin(π/2-θ) Tanθ=cot(π/2-θ) Cscθ=sin(π/2-θ) Secθ=Csc(π/2-θ) Cotθ=Tan(π/2-θ)

Half Angle Formulas

sin θ/2 = + or - √(1 - cos θ)/2 cos θ/2 = + or - √1 + cos θ)/2 tan θ/2 = + or - √1-cosθ/1+cosθ =(1 - cos θ)/(sin θ) or (sin θ)/(1 + cos θ)

Sum and Difference Identities

sin(α ± β) = sin(α)cos(β) ± cos(α)sin(β) cos(α ± β) = cos(α)cos(β) ∓ sin(α)sin(β) Tan(α ± β)= tan(α) ± tan(β)/1∓tan(α)tan(β)

Reciprocal Identities

sinθ = 1/cscθ ; cscθ = 1/sinθ cosθ = 1/secθ ; secθ = 1/cosθ tanθ = 1/cotθ ; cotθ = 1/tanθ

Quotient Identities

tanθ = sinθ/cosθ cotθ = cosθ/sinθ