What is $\displaystyle cos 480$ in terms of $\displaystyle sin$?
$\displaystyle \cos (480 ^\circ) = -\frac{1}{2}$
$\displaystyle \sin ^{-1} (-\frac{1}{2}) = -30^\circ = 210^\circ =330^\circ= 570^\circ$
But for unit circle, we select $\displaystyle -30^\circ $ as we are measure as close to zero as possible. In other words, the range of $\displaystyle \sin ^{-1}$ is restricted to [–90°, 90°].