Answer
Exact value of $\sin \frac{3\pi}{2} = -1$
Work Step by Step
To find exact value of $\sin \frac{3\pi}{2}$, let's find its reference angle first.
The reference angle = $2\pi - \frac{3\pi}{2}$ = $\frac{\pi}{2}$
As $ \frac{3\pi}{2}$ terminates in between quadrant III and quadrant IV and in both cases its $\sin$ will be negative. Therefore by reference angle theorem-
$\sin \frac{3\pi}{2}$ = - $\sin\frac{\pi}{2}$
= - $1$
