Six different proofs of the Pythagorean theorem. | Visual Math

The Pythagorean identity is one of the most fundamental relationships in trigonometry. It states that for any angle θ, the sum of the squares of sine and cosine equals one: sin²(θ) cos²(θ) = 1. This identity is derived directly from the Pythagorean theorem, which relates the sides of a right triangle. If we consider a point (x, y) on the unit circle (a circle with radius 1 centered at the origin), then x = cos(θ) and y = sin(θ). By the definition of the circle, x² y² = 1², which becomes cos²(θ)