1. **State the problem:** Find the cosine of the complement of each given angle. 2. **Recall the complement rule:** The complement of an angle $\theta$ is $90^\circ - \theta$. 3. **Formula for cosine of complement:** $$\cos(90^\circ - \theta) = \sin(\theta)$$ This is a fundamental trigonometric identity. 4. **Calculate for each angle:** **a. For $30^\circ$:** $$\cos(90^\circ - 30^\circ) = \cos(60^\circ) = \sin(30^\circ)$$ We know $\sin(30^\circ) = \frac{1}{2}$. **b. For $45^\circ$:** $$\cos(90^\circ - 45^\circ) = \cos(45^\circ) = \sin(45^\circ)$$ We know $\sin(45^\circ) = \frac{\sqrt{2}}{2} \approx 0.7071$. 5. **Final answers:** - a. $0.5$ - b. $0.7071$