Answer
$$ - \frac{\pi }{2}$$
Work Step by Step
$$\eqalign{
& {\text{Let }}y = {\sin ^{ - 1}}\left( { - 1} \right) \cr
& {\text{Use the even/odd property}} \cr
& {\text{ }}y = - {\sin ^{ - 1}}\left( 1 \right) \cr
& {\text{In the interval }}\left[ { - \frac{\pi }{2},\frac{\pi }{2}} \right]{\text{ }}\sin \theta = 1{\text{ for }}\theta = \frac{\pi }{2},{\text{ then}} \cr
& {\sin ^{ - 1}}\left( { - 1} \right) = - \frac{\pi }{2} \cr} $$
