1. **Problem Statement:** Given that $\sin \theta = \frac{3}{5}$ and $\theta$ is in the first quadrant, find $\cos \theta$. 2. **Formula and Rules:** We use the Pythagorean identity: $$\sin^2 \theta + \cos^2 \theta = 1$$ This identity holds for all angles $\theta$. 3. **Substitute the given value:** $$\left(\frac{3}{5}\right)^2 + \cos^2 \theta = 1$$ $$\frac{9}{25} + \cos^2 \theta = 1$$ 4. **Solve for $\cos^2 \theta$:** $$\cos^2 \theta = 1 - \frac{9}{25} = \frac{25}{25} - \frac{9}{25} = \frac{16}{25}$$ 5. **Find $\cos \theta$:** $$\cos \theta = \pm \sqrt{\frac{16}{25}} = \pm \frac{4}{5}$$ 6. **Determine the sign:** Since $\theta$ is in the first quadrant, both sine and cosine are positive. Therefore, $$\cos \theta = \frac{4}{5}$$ **Final answer:** $\boxed{\frac{4}{5}}$ which corresponds to option b.