SOLUTION: Find the exact value of sin &#952;/2 if cos &#952; = 2/3 and 270º< &#952;<360º. Thank You

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Question 42454: Find the exact value of sin θ/2 if cos θ = 2/3 and 270º< θ<360º.
Thank You
Answer by fractalier(2101) About Me  (Show Source):
You can put this solution on YOUR website!
Let q be theta...
sin q/2 = ± sqrt((1 - cos q) / 2)
sin q/2 = ± sqrt((1 - 2/3) / 2)
sin q/2 = ± sqrt(1/6) = ± sqrt(6) / 6
In the 4th quadrant, sin is negative, but in the 2nd quadrant, where q/2 is, the sin is positve, thus
sin q/2 = sqrt(6) / 6