Answer
$-\frac{\sqrt {5}}{2}$
Work Step by Step
Recall that $1+\cot^{2}\theta=\csc^{2}\theta$
$\implies 1+(-\frac{1}{2})^{2}=\frac{5}{4}=\csc^{2}\theta$
$\implies \csc\theta=\pm \sqrt {\frac{5}{4}}=\pm\frac{\sqrt 5}{2}$
$\csc\theta$ is negative in the fourth quadrant.
$\implies \csc\theta=-\frac{\sqrt {5}}{2}$
