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

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.