# How do you evaluate sin(cos^-1(3/5))?

Jun 30, 2016

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

#### Explanation:

For evaluating $\sin \left({\cos}^{- 1} \left(\frac{3}{5}\right)\right)$, let us assume

$\cos x = \frac{3}{5}$ hence $x = {\cos}^{- 1} \left(\frac{3}{5}\right)$ and

$\sin x = \pm \sqrt{1 - {\left(\frac{3}{5}\right)}^{2}} = \pm \sqrt{1 - \frac{9}{25}} = \pm \sqrt{\frac{16}{25}} = \pm \frac{4}{5}$

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