1. **Problem:** Given $\sin \theta = \frac{3}{5}$ and $\theta$ is in quadrant I, find $\cos 2\theta$. 2. **Formula:** Use the double-angle identity for cosine: $$\cos 2\theta = 1 - 2\sin^2 \theta$$ 3. **Step 1:** Calculate $\sin^2 \theta$: $$\sin^2 \theta = \left(\frac{3}{5}\right)^2 = \frac{9}{25}$$ 4. **Step 2:** Substitute into the formula: $$\cos 2\theta = 1 - 2 \times \frac{9}{25} = 1 - \frac{18}{25}$$ 5. **Step 3:** Simplify: $$\cos 2\theta = \frac{25}{25} - \frac{18}{25} = \frac{7}{25}$$ 6. **Answer:** $$\boxed{\cos 2\theta = \frac{7}{25}}$$ This completes the solution for the first question.