1. **Stating the problem:** We are given that $\cos(45^\circ) = \sin(\theta)$ and need to find the value of $\theta$. 2. **Recall the identity:** $\sin(\theta) = \cos(90^\circ - \theta)$. 3. Using this identity, we can write: $$\cos(45^\circ) = \sin(\theta) = \cos(90^\circ - \theta)$$ 4. Since $\cos(45^\circ) = \cos(90^\circ - \theta)$, the angles must be equal or supplementary: $$45^\circ = 90^\circ - \theta \quad \text{or} \quad 45^\circ = -(90^\circ - \theta)$$ 5. Solve the first equation: $$45^\circ = 90^\circ - \theta \implies \theta = 90^\circ - 45^\circ = 45^\circ$$ 6. Solve the second equation: $$45^\circ = -90^\circ + \theta \implies \theta = 45^\circ + 90^\circ = 135^\circ$$ 7. Since $\theta$ is typically between $0^\circ$ and $90^\circ$ for this problem, the valid solution is: $$\boxed{45^\circ}$$ **Answer:** $\theta = 45^\circ$.