Chapter 14.1, Problem 60SR

To determine

To find:Value of $\cos \left(\text{Arcsin}\left(\frac{3}{5}\right)\right)$

Answer to Problem 60SR

  $\frac{\text{4}}{5}$

Explanation of Solution

Given information:

We know that, the given expression is $\cos \left({\text{sin}}^{-1}\left(\frac{3}{5}\right)\right)$

Calculation :

  $\begin{array}{l}\Rightarrow \cos \left(\text{Arcsin}\left(\frac{3}{5}\right)\right)\\ \Rightarrow \cos \left({\text{sin}}^{-1}\left(\frac{3}{5}\right)\right)\\ \text{Let}si{n}^{-1}\frac{3}{5}=\text{θ}\\ \frac{3}{5}=\sin \text{θ}=\frac{\text{Perpendicular}}{\text{Hypotenuse}}\\ \Rightarrow \cos \text{θ=}\frac{4}{5}\\ \therefore \cos \left({\text{sin}}^{-1}\left(\frac{3}{5}\right)\right)=\frac{4}{5}\end{array}$