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Pythagorean Identity

Pythagorean Identity 2

From the diagram below, we can see that the triangle has horizontal and vertical sides of length $\sin(\theta)$ and $\cos(\theta)$. We now note that the triangle is a right-angled triangle and that the circle has a radius of 1. It follows that $$ (\sin(\theta))^2 + (\cos(\theta))^2 \equiv 1 $$ This is true irrespective of the value of $\theta$

pythagorean identity