Answer
$-0.73$
Work Step by Step
Note that $\csc {x}=\frac{1}{\sin{(x)}}$.
Hence, $\csc^{-1}{x}=\sin^{-1} {\left(\frac{1}{x}\right)}$.
Use a calculator in radian mode and round the result to decimal places to obtain
$\csc^{-1}{(-\frac{3}{2})}=\sin^{-1} {\left(\dfrac{1}{-\frac{3}{2}}\right)}=-0.7297\approx-0.73$