Answer
$1$
Work Step by Step
We know that $\sin$, $\csc$, $\tan$ are odd functions, which means $f(-\theta)=-f(\theta).$
We also know that $\cos$, $\sec$, are even functions, which means $f(-\theta)=f(\theta).$
Therefore,
$\sin{\left(-\frac{3\pi}{2}\right)}=-\sin{\left(\frac{3\pi}{2}\right)}=-(-1)=1$
