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Math Help - Inverse Trig Function Question

  1. #1
    Junior Member
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    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?
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    Start by showing that \csc \alpha = \frac{{\sqrt {1 + \tan ^2 \alpha } }}<br />
{{\tan \alpha }} \implies \csc (\arctan \alpha ) = \frac{{\sqrt {1 + \alpha ^2 } }}<br />
{\alpha }.

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