Question

How do you find the exact values of sin 22.5 ° using the half angle formula?

Answer 1

I found: `0.382`

Explanation:

Using the half angle formula you get:
`sin^2(theta)=1/2[1-cos(2theta)]`
if `theta=22.5°` then `2theta=45°`
so you get:
`sin^2(22.5°)=1/2[1-cos(45°)]`
`sin^2(22.5°)=1/2[1-sqrt(2)/2]=(2-sqrt(2))/4`
and square root both sides:
`sin(22.5°)=+-sqrt((2-sqrt(2))/4)=+-0.382`
so `sin(22.5°)=0.382`