How do you solve cos(Sin^-1(2x))?

Question

The variable x is confusing me~

Answer 1

to solve these types of problems, work from the inside out.

let's find inverse sin (arcsin) 2x = θ

first determine the lengths of all the sides of a right triangle using the information inverse sin (arcsin) of 2x.

This means there is an angle θ whose sin is 2x. We don't need to know the exact value of this angle. We only need to draw a triangle with an angle θ so that sin (opposite over hypotenuse) equals 2x.

this means the opposite side has a length 2x and the hypotenuse has length 1. Because then opposite over hypotenuse is 2x / 1 = 2x.

 

Now we can determine the adjacent side using Pythagorean theorem

 

a² + (2x)² = 1²

a² = 1 - 4x²

a = √(1 - 4x²)

 

now we have cos θ = adjacent over hypotenuse = √(1 - 4x²)

 

 

Answer 2

 

To Solve Cos(Sin^-1(2x))=k

Work with:

Assume: Sin^-1(2x)=k₁

Assume: 2x=k₂

 

Solve:

Cos(k₁) = k ....1st

keep working till you get x in terms of k, eliminating k₁ and k₂.

 

Hope this helps.