1. Given that $ \sin \theta = \frac{4}{5} $, we need to find $ \tan \theta $ and $ \cos \theta $. 2. Recall the Pythagorean identity: $$\sin^2 \theta + \cos^2 \theta = 1$$ This means we can find $ \cos \theta $ by rearranging: $$\cos \theta = \sqrt{1 - \sin^2 \theta}$$ 3. Substitute $ \sin \theta = \frac{4}{5} $: $$\cos \theta = \sqrt{1 - \left(\frac{4}{5}\right)^2} = \sqrt{1 - \frac{16}{25}} = \sqrt{\frac{9}{25}} = \frac{3}{5}$$ 4. Now, $ \tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{\frac{4}{5}}{\frac{3}{5}} $. Cancel the common denominator 5: $$\tan \theta = \frac{4}{\cancel{5}} \times \frac{\cancel{5}}{3} = \frac{4}{3}$$ **Final answers:** (a) $ \tan \theta = \frac{4}{3} $ (b) $ \cos \theta = \frac{3}{5} $