# Fundamental Identities & Proving Trigonometric Tautologies

Pythagorean Identity.  This identity is so named because we can read it off of the unit circle by looking at any of the right triangles and remembering the Pythagorean Theorem.

1.   $\rhd$ Proof of the pythagorean identity $\sin^2(\theta) + \cos^2(\theta) = 1$ (6:12)
2.   $\rhd$ Using the Pythagorean trig identity (6:15)
Given that $\sin(\theta) = \frac{1}{2}$ and that $\theta$ is in the third quadrant, Sal finds $\tan(\theta)$.
3.   $\star$ Solving problems of the type: given that $\theta$ is in the third quadrant and that $\cos(\theta) = \frac{-12}{13}$, find $\sin(\theta)$.