How to express $\cos\left(\frac{3\pi}{2} + x\right)$ in terms of $\sin x$ and $\cos x$

Question

Express $$\cos \Bigg(\frac{3\pi}{2} + x\Bigg)$$ in terms of $\sin x$ and $\cos x$

My try:

$$\cos \Big(\frac{3\pi}{2} + x\Big)=\cos \frac{3\pi}{2} \cos x-\sin \frac{3\pi}{2} \sin x=0-(-1)\sin x=\sin x$$

Is this the correct way to do it?

Answer 1

Recall the identities for sine and cosine in the four quadrants. One of the QIV identities is the following. $$\cos\big(\frac{3\pi}{2}+x\big) = \sin x$$