# How do you find the exact values of sintheta and tantheta when costheta=2/5?

Feb 11, 2017

$\sin \theta = \frac{\sqrt{21}}{5}$
$\tan \theta = \frac{\sqrt{21}}{2}$

#### Explanation:

We need

${\sin}^{2} \theta + {\cos}^{2} \theta = 1$

$\tan \theta = \sin \frac{\theta}{\cos} \theta$

$\cos \theta = \frac{2}{5}$

$\sin \theta = \sqrt{1 - {\cos}^{2} \theta}$

$= \sqrt{1 - \frac{4}{25}} = \sqrt{\frac{21}{25}}$

$= \frac{\sqrt{21}}{5}$

$\tan \theta = \sin \frac{\theta}{\cos} \theta = \frac{\frac{\sqrt{21}}{5}}{\frac{2}{5}}$

$= \frac{\sqrt{21}}{2}$