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?
Start by showing that $\displaystyle \csc \alpha = \frac{{\sqrt {1 + \tan ^2 \alpha } }}
{{\tan \alpha }} \implies \csc (\arctan \alpha ) = \frac{{\sqrt {1 + \alpha ^2 } }}
{\alpha }.$
So $\displaystyle \csc \left[ {\arctan \left( { - \frac{5}
{3}} \right)} \right] = - \frac{{\sqrt {1 + \dfrac{{25}}
{9}} }}
{{\dfrac{5}
{3}}} = - \frac{{\sqrt {34} }}
{5}.$