Prove: $\sin (3\pi/2 - x) = -\cos(x)$

Question

I know the sine of $3\pi/2$ is $-1$.

So i plug it in the function making it. $\sin(-1-x) = -\cos x$.

However, I don't know where to go from here.

Answer 1

Hint

Do you know that

$$\sin(\pi+x)=-\sin x$$ and $$\sin\left(\frac\pi2-x\right)=\cos x\qquad?$$

if NO, draw the trigonometric circle!