Answer
$-1$
Work Step by Step
We know that $csc$ has a period of $2\pi$, hence first we try and find a value where the argument is between $0$ and $2/pi$. Therefore $csc(\frac{11\pi}{2})=csc(\frac{(11-4)\pi}{2})=csc(\frac{7\pi}{2})=csc(\frac{(7-4)\pi}{2})=csc(\frac{3\pi}{2})=-1.$
