Answer
-1
Work Step by Step
We can find the cosecant of coterminal angle that lies between $0^{\circ}$ and $360^{\circ}$ for convenience.
$\csc(-450^{\circ})= \csc(-450^{\circ}+2\cdot360^{\circ})=\csc 270^{\circ}$
The terminal side of $270^{\circ}$ angle passes through (0,-1). So $x=0,y=-1$ and $r=1$.
$\csc 270^{\circ}=\frac{r}{y}=\frac{1}{-1}=-1$
