Pythagorean identity: sin²θ + cos²θ = 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.
Related Pythagorean identities
Common questions
What is the sin²θ + cos²θ = 1 identity?
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.
Which identities are related to sin²θ + cos²θ = 1?
sin²θ + cos²θ = 1 belongs to the Pythagorean group. The identities used alongside it most often are 1 + tan²θ = sec²θ and 1 + cot²θ = csc²θ.
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.