Question

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

Answer 1

`4/5`

Explanation:

First consider that : `theta=arcsin(3/5)`

`theta` just represents an angle.

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

If `theta=arcsin(3/5)` then,

`=>sin(theta)=3/5`

To find `cos(theta)` We use the identity : `cos^2(theta)=1-sin^2(theta)`

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

`=>cos(theta)=sqrt(1-(3/5)^2)=sqrt((25-9)/25)=sqrt(16/25)=color(blue)(4/5)`