Trig identities

sin² + cos² = 1, and the family of equations that always hold.

Equations involving trig functions that hold for every angle.

Graph

y = sin(x)·sin(x)y = (1 - cos(2·x))/2

Both curves above lie exactly on top of each other — that's a visual proof that sin²x = (1 − cos 2x)/2 for every x. An identity is an equation that's true everywhere, not just at certain solutions.

The ones worth memorising

sin^{2} θ + cos^{2} θ = 1 sin 2 θ = 2 sin θ cos θ cos 2 θ = cos^{2} θ - sin^{2} θ = 1 - 2 sin^{2} θ

Everything else can be derived from the Pythagorean and angle-sum identities.

Your turn

Given sin θ = 3/5 and θ is acute, find cos θ.

Pythagorean

sin^{2} θ + cos^{2} θ = 1

Angle sum

sin (A + B) = s in A cos B + cos A s in B

Double angle

cos (2 θ) = cos^{2} θ - sin^{2} θ

Unit circle Sin, cos, tan graphs Trigonometry

Trig identities

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