# The Pythagorean Theorem and the Unit Circle

This following diagram shows that $\displaystyle \sin^2 \theta + \cos^2 \theta = 1$, given $\displaystyle \cos \theta \equiv \frac{adj}{hyp}$ and $\displaystyle \sin \theta \equiv \frac{opp}{hyp}$ and the Pythagorean theorem. Here, $opp$, $hyp$, and $adj$ are variables for lengths. The values corresponding to these lengths are positive numbers or zero.

#### Written by Christina Daniel

I am a research assistant in theoretical physics. This website, derive-it.com, serves to organize my ongoing learning and research as well as to provide a resource to other learners around the world.