Answer
$\csc$ -855$^{\circ}$ = -$\sqrt2$
Work Step by Step
$\csc$ -855$^{\circ}$
First, lets find the coterminal angle.
-855$^{\circ}$ - 3(360$^{\circ}$) = 225$^{\circ}$
Next, we find the reference angle.
$\theta$$^{1}$ = 225$^{\circ}$ - 180$^{\circ}$ = 45$^{\circ}$
Since the coterminal angle is in Quadrant III, $\csc$ is negative.
Therefore:
$\csc$ 45$^{\circ}$ = -$\sqrt2$
