Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$-0.34$
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, $\csc^{-1} {-3} = \sin^{-1} {\left(-\frac{1}{3}\right)} \approx \boxed{-0.34}$