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

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

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Answer 1 · 2015-07-28T15:59:53

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.

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

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