Answer
-1
Work Step by Step
We can find the cosine of coterminal angle that belongs to [$0^{\circ}$,$360^{\circ}$) for convenience.
$\cos(-900^{\circ})= $
$\cos(-900^{\circ}+3\cdot360^{\circ})=\cos 180^{\circ}$
The terminal side of $180^{\circ}$ angle passes through (-1,0). So $x=-1,y=0$ and $r=1$.
$\cos 180^{\circ}=\frac{x}{r}=\frac{-1}{1}=-1$
