# How do you find the exact values of costheta and tantheta when sintheta=-2/3?

Dec 30, 2016

$\cos \theta = \pm \frac{\sqrt{5}}{3}$ and $\tan \theta = \pm \frac{2 \sqrt{5}}{5}$
${\cos}^{2} \theta = 1 - {\sin}^{2} \theta$
${\cos}^{2} \theta = 1 - \frac{4}{9} = \frac{5}{9}$
$\cos \theta = \pm \frac{\sqrt{5}}{3}$
$\tan \theta = \sin \frac{\theta}{\cos \theta} = \pm \left(\frac{2}{3}\right) \left(\frac{3}{\sqrt{5}}\right) = \pm \frac{2}{\sqrt{5}} = \pm \frac{2 \sqrt{5}}{5}$