Answer
1.483014
Work Step by Step
Converting $-317^{\circ}36'$ to decimal degrees, we get
$-317^{\circ}36'=-(317^{\circ}+\frac{36}{60}^{\circ})=-(317^{\circ}+0.6^{\circ})=-317.6^{\circ}$
$\csc(-317^{\circ}36')=\csc(-317.6^{\circ})=\frac{1}{\sin (-317.6^{\circ})}\approx1.483014$
