# How do you find the value of cot theta given csc theta=-2 and in quadrant IV?

Dec 13, 2016

$- \sqrt{3}$
$\csc t = - 2$ --> $\sin t = \frac{1}{\csc t} = - \frac{1}{2}$.
${\cos}^{2} t = 1 - {\sin}^{2} t = 1 - \frac{1}{4} = \frac{3}{4}$
$\cos t = \pm \frac{\sqrt{3}}{2}$
$\cot t = \frac{\cos}{\sin} = \left(\frac{\sqrt{3}}{2}\right) \left(- \frac{2}{1}\right) = - \sqrt{3}$