SOLUTION: what is the exact value of sin 22.5 degrees using the sum, difference, half, or double angle formulas and the exact value chart in the solution.

Question 34739: what is the exact value of sin 22.5 degrees using the sum, difference, half, or double angle formulas and the exact value chart in the solution.
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
what is the exact value of sin 22.5 degrees using the sum, difference, half, or double angle formulas and the exact value chart in the solution.
LET A = 22.5...LET SIN(A)=X TO BE FOUND OUT..
2A=2*22.5=45
COS(2A)=1-2*{SIN(A)}^2
COS(45)=1-2X^2
1/SQRT(2)=1-2X^2
2X^2=1-1/SQRT(2)=1-SQRT(2)/2=(2-SQRT(2))/2
X^2=(2-SQRT(2))/4
X=SQRT{2-SQRT(2)}/2
=0.3827
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