Question

How do you find the exact values of sin^2(pi/8) using the half angle formula?

Answer 1

I found: `sin(pi/8)=0.3827`

Explanation:

The half angle formula is:
`color(red)(sin^2(x)=1/2[1-cos(2x)]`
if:
`x=pi/8`
then `2x=2pi/8=pi/4`
You get:
`sin^2(pi/8)=1/2[1-cos(pi/4)]`
but `cos(pi/4)=sqrt(2)/2`
giving:
`sin^2(pi/8)=1/2[1-sqrt(2)/2]=(2-sqrt(2))/4`
and: `sin(pi/8)=+-sqrt((2-sqrt(2))/4)=+-0.3827`. I choose the positive one.