# How do you calculate tan(cos^-1(-3/5))?

Jul 22, 2015

$\tan \left({\cos}^{- 1} \left(- \frac{3}{5}\right)\right) = \pm \frac{4}{3}$

#### Explanation:

If $\cos \left(\theta\right) = - \frac{3}{5}$
then $\theta$ must be one of the angles indicated in the diagram below (either in the second or third quadrant).

Both associate triangles are standard $3 - 4 - 5$ right angled triangles
and depending upon whether the angle is in the second or third quadrant,
the $\tan$ will be either $\frac{4}{5}$ or $- \frac{4}{5}$