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?

1 Answer

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