# Thread: Inverse Trig Function Question

1. ## Inverse Trig Function Question

I've been trying to figure this out, but I have yet to find an answer.

The question is:

Determine the value of csc(arctan (-5/3)).

Does anyone have any suggestions?

2. Start by showing that $\csc \alpha = \frac{{\sqrt {1 + \tan ^2 \alpha } }}
{{\tan \alpha }} \implies \csc (\arctan \alpha ) = \frac{{\sqrt {1 + \alpha ^2 } }}
{\alpha }.$

So $\csc \left[ {\arctan \left( { - \frac{5}
{3}} \right)} \right] = - \frac{{\sqrt {1 + \dfrac{{25}}
{9}} }}
{{\dfrac{5}
{3}}} = - \frac{{\sqrt {34} }}
{5}.$