Answer
$-0.73$
Work Step by Step
Let $\theta = \csc^{-1} {\left(-\frac{3}{2}\right)}$
Then, $\csc{\theta} = -\dfrac{3}{2}$.
Since $\sin{\theta}= \dfrac{1}{\csc{\theta}}$, then
$\sin{\theta} = -\dfrac{2}{3}$
Thus,
$\theta = \sin^{-1} {\left(-\frac{2}{3}\right)}\approx -0.73$
Hence,
$\csc^{-1} {\left(-\frac{3}{2}\right)}= \sin^{-1} {\left(-\frac{2}{3}\right)} \approx \boxed{-0.73}$
