Question

How do you use the half angle identity to find exact value of cos22.5 degrees?

Answer 1

I found: `cos(22.5°)=0.9238`

Explanation:

Using the half angle formula:
`cos^2(x)=1/2(1+cos(2x))`
Using your angle `x=22.5°` and `2x=45°` you get:
`cos^2(22.5°)=1/2(1+cos(45°))`
But `cos(45°)=sqrt(2)/2`
So:
`cos^2(22.5°)=(2+sqrt(2))/4`
`cos(22.5°)=sqrt((2+sqrt(2))/4)~~0.9238`