SOLUTION: Use a half angle identity to find the exact value of cos(19pi/12)

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Question 883169: Use a half angle identity to find the exact value of cos(19pi/12)
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Use a half angle identity to find the exact value of cos(19pi/12)
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Note: cos(t/2) = +/-sqrt[(1+cos(t))/2]
If t/2 = 19pi/12, t = 19pi/6
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But 19pi/6 = 2pi + (7/6)pi
And cos(7pi/6) = -cos(pi/6) = -sqrt(3)/2
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So cos(19pi/12) = sqrt[(1-sqrt(3)/2))/2] = sqrt(2-sqrt(3))/4)
= sqrt(2-sqrt(3))/2
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Cheers,
Stan H.