Answer
$-1$
Work Step by Step
We need to compute $\csc (\dfrac{11 \pi}{2})$
The trigonometric function $\csc$ has a period of $2\pi$. Thus, we can simplify as follows:
$\csc (\dfrac{11 \pi}{2})=\csc (\dfrac{3\pi}{2}+\dfrac{8 \pi}{2}) \\ =\csc (\dfrac{3\pi}{2}+4\pi) \\ =\csc \dfrac{3\pi}{2} \\=-1$
