Answer
$-2$
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,
$\csc(-30^{o})=-\csc(30^{o})=-\dfrac{1}{\sin(30^{o})}=-\dfrac{1}{\frac{1}{2}}=-2$