Pythagorean

Pythagorean identity: sin²θ + cos²θ = 1

sin2θ+cos2θ=1\sin^{2}\theta + \cos^{2}\theta = 1

The Pythagorean identity says sin²θ + cos²θ = 1 for every angle θ - it is the Pythagorean theorem read off the unit circle, where sine and cosine are the legs and the radius is 1. It is the most-used identity in the subject: rearranged it converts any sine into a cosine (and back), which is how most simplification and integration problems get started.

fundamental

Related Pythagorean identities

Practise it

Reading a formula is not the same as recalling it under time pressure. The workspace drills Pythagorean questions in the quiz, and the triangle solver shows a worked solution for any triangle you type in.

Or browse all 45 identities in the full reference, or read the trigonometry guides for the method behind them.