SOLUTION: Theta = x If x is an acute angle with cos x = 1/9, find the exact value of sin a/2.

Question 69491: Theta = x
If x is an acute angle with cos x = 1/9, find the exact value of sin a/2.
Found 2 solutions by Nate, stanbon:
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
sin^2(0.5x) = 0.5(1 - cos(x))
sin^2(0.5x) = 0.5(1 - 1/9)
sin^2(0.5x) = 0.5(8/9)
sin^2(0.5x) = 4/9
sin(0.5x) = +- 2/3
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Theta = x
If x is an acute angle with cos x = 1/9, find the exact value of sin a/2.
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COMMENT: I'm going to assume your "sin a/2" should be sin x/2.
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sin(x/2) = sqrt[(1-cos(x))/2]
sin(x/2) = sqrt[(1-(1/9))/2]
sin(x/2) = sqrt[8/18]=sqrt(4/9)=2/3
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Cheers,
Stan H.
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