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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 $y=\sin^2 \frac{\theta}{2}$?

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