Trig Identities Calculator

Reference the most useful trigonometric identities for algebra and calculus.

Last updated: June 2026 | By Patchworkr Team

Pythagorean Identities

sin^2(θ) + cos^2(θ) = 1

1 + tan^2(θ) = sec^2(θ)

1 + cot^2(θ) = csc^2(θ)

sin(θ) = 1 / csc(θ)

cos(θ) = 1 / sec(θ)

tan(θ) = 1 / cot(θ)

tan(θ) = sin(θ) / cos(θ)

cot(θ) = cos(θ) / sin(θ)

sin(2θ) = 2sin(θ)cos(θ)

cos(2θ) = cos^2(θ) - sin^2(θ)

tan(2θ) = 2tan(θ) / (1 - tan^2(θ))

sin(θ/2) = ±√((1 - cos(θ)) / 2)

cos(θ/2) = ±√((1 + cos(θ)) / 2)

tan(θ/2) = sin(θ) / (1 + cos(θ))

Reference guide

Common trig identities in one place

Trigonometric identities are equations that are true for every valid angle.

They help simplify expressions and solve problems faster.

Yes, for all valid angles where the expressions are defined.

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