Question

Solve without a calculator. cos(arcsin (3x/2))

I made a triangle but im stuck after that..

Answer 1

arcsin (3x/2) is base angle Ø of a right angled-triangle, so that the opposite side is 3x and the hypotenuse is 2
So find the third side using Pythagoras, that would be
√(4 - 9x^2)

so cos Ø = √(4-9x^2)/2
or
cos (arcsin (3x/2)) = √(4-9x^2)/2