Answer
Please refer to the step-by-step part below.
Work Step by Step
Recall:
(1) $\cos{(\alpha+\beta)}=\cos{(\alpha)}\cos{(\beta)}-\sin{(\alpha)}\sin{(\beta)}$
(2) $\cos{\frac{3\pi}{2}}=0$ and $\sin{\frac{3\pi}{2}}=-1$
Hence,
$\cos{(\frac{3\pi}{2}+\theta)}\\=\cos{(\frac{3\pi}{2})}\cos{(\theta)}-\sin{(\frac{3\pi}{2})}\sin{(\theta)}\\=0\cos{(\theta)}-(-1)\cdot \sin{(\theta)}\\
=\sin{(\theta)}$
