### Trigonometry: Compound Angles

Many ways problem

## Problem

Take a look at these identities.

$\cos^2 \frac{\theta}{2} \equiv \frac{1}{2}(1+\cos \theta) \quad \quad \quad \sin^2 \frac{\theta}{2} \equiv \frac{1}{2}(1-\cos \theta)$

How could you use these identities to help you sketch graphs of $y=\cos^2 \frac{\theta}{2}$ and $y=\sin^2 \frac{\theta}{2}$?

The resource Proving half-angle formulae looks at a way to prove these identities geometrically.