# What is  cos (Arcsin (3/5))?

Jul 21, 2015

$\frac{4}{5}$

#### Explanation:

First consider that : $\theta = \arcsin \left(\frac{3}{5}\right)$

$\theta$ just represents an angle.

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

If $\theta = \arcsin \left(\frac{3}{5}\right)$ then,

$\implies \sin \left(\theta\right) = \frac{3}{5}$

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

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

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