Rewrite cos(arcsin(v)) as an algebraic expression in v.

i know that the answer is squroot of 1-v^2

but i don't know the process of how to come to this answer. Thanks for the help!

2 answers

Hehehe!!

My math skills stop at elementary math. I have no idea how to help you with this problem!
arcsin(v) or arcsin(v/1) is the angle x so that
sin x = v/1

sketch a rightangled triangle where the hypotenuse is 1 and the side opposite angle x is v
let the adjacent side by k

then by Pythagoras,
k^2 + v^2 = 1^2
k^2 = 1 - v^2
k = √(1 - v^2)

so cosx
= cos(sinarc(v)) = k/1 = √(1 - v^2)