Question 925014: Given sin(alpha)=3/4 and 0
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Given sin(alpha)=3/4 and 0 < alpha < pi, find the exact value of sin(alpha/2). Note: You are not allowed to use decimals in your answer.
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sin(a/2) = sqrt[(1-cos(a))/2]
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Since sin(a) = 3/4, and 0 < alpha < pi,
cos(a) = +/-sqrt(4^2-3^2)/4 = +/-sqrt(7)/4
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So, sin(a/2) = sqrt[(1+/-sqrt(7)/4)/2]
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Note:: Since 0 < alpha < pi, cos(a) could be positive or it could be negative.
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Cheers,
Stan H.
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