Answer
$-0.34$
Work Step by Step
Let $\theta = \csc^{-1} {-3}$
Then, $\csc{\theta} = -3$.
Since $\sin{\theta}= \dfrac{1}{\csc{\theta}}$, then
$\sin{\theta} = -\dfrac{1}{3}$
Thus,
$\theta = \sin^{-1} {\left(-\frac{1}{3}\right)}\approx -0.34$
Hence,
$\csc^{-1} {-3} = \sin^{-1} {\left(-\frac{1}{3}\right)} \approx \boxed{-0.34}$