Applications of the Unit Circle

The identify $\cos^2 \theta + \sin^2 \theta = 1$ is required for finding trigonometric ratios.

Example 1

Find exactly the possible values of $\cos \theta$ for $\sin \theta = \dfrac{5}{8}$.

Example 2

If $\sin \theta = -\dfrac{2}{3}$ and $\pi \lt \theta \lt \dfrac{3 \pi}{2}$, find the exact values of $\cos \theta$ and $\tan \theta$.

Example 3

If $\tan \theta = -3$ and $\dfrac{3 \pi}{2} \lt \theta \lt 2 \pi$, find the exact values of $\sin \theta$ and $\cos \theta$.