SOLUTION: Find the exact value by using half-angle formula. a)sin22.5 b)sin7pie/8

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Question 39058: Find the exact value by using half-angle formula.
a)sin22.5 b)sin7pie/8
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the exact value by using half-angle formula.
a)sin22.5=sin(45/2)= sqrt[(1-cos(45))/2]
= sqrt[(1-(sqrt(2)/2))/2]=[sqrt[(2-sqrt(2)]]/2
=0.38268343...
b)sin(7pie/8)= sin[(1/2)(7pi/4)]=
sqrt[(1-cos(7pi/4))/2]=sqrt[1-(sqrt(2)/2)/2]
=[sqrt[2-sqrt(2)]]/2=0.38268343...
Cheers,
Stan H.