Question

What is `sin(arccos(5/13))`?

Answer 1

`12/13`

Explanation:

First consider that : `theta=arccos(5/13)`

`theta` just represents an angle.

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

If `theta=arccos(5/13)` then,

`=>cos(theta)=5/13`

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

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

`=>sin(theta)=sqrt(1-(5/13)^2)=sqrt((169-25)/169)=sqrt(144/169)=color(blue)(12/13)`