# What is cos[Arcsin(-4/5)]?

Jul 21, 2015

$\frac{3}{5}$

#### Explanation:

First consider that : $\epsilon = \arcsin \left(- \frac{4}{5}\right)$

$\epsilon$ simply represents an angle.

This means that we are looking for color(red)cos(epsilon)!

If $\epsilon = \arcsin \left(- \frac{4}{5}\right)$ then,

$\implies \sin \left(\epsilon\right) = - \frac{4}{5}$

To find $\cos \left(\epsilon\right)$ We use the identity : ${\cos}^{2} \left(\epsilon\right) = 1 - {\sin}^{2} \left(\epsilon\right)$

=>cos(epsilon)=sqrt(1-sin^2(epsilon)

$\implies \cos \left(\epsilon\right) = \sqrt{1 - {\left(- \frac{4}{5}\right)}^{2}} = \sqrt{\frac{25 - 16}{25}} = \sqrt{\frac{9}{25}} = \textcolor{b l u e}{\frac{3}{5}}$