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

1 Answer
Jul 28, 2015

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.