Question

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

Answer 1

`3/5`

Explanation:

First consider that : `epsilon=arcsin(-4/5)`

`epsilon` simply represents an angle.

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

If `epsilon=arcsin(-4/5)` then,

`=>sin(epsilon)=-4/5`

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

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

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