Question 1033303: Use the half-angle identity to find the exact value of cos([7pi]/[12])
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Use the half-angle identity to find the exact value of cos([7pi]/[12])
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cos[7pi/6] = ?
Reference angle = pi/6
7pi/6 is in QIII where cos is negative
So, cos[7pi/6] = -cos(pi/6) = -sqrt(3)/2
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Note:: 7pi/12 = (1/2)[7pi/6]
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Formula:: cos(x/2) = sqrt[(1+cos(x)/2])
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Therefore:: cos[7pi/12] = cos[(7pi/6)/2] = sqrt[(1+cos(7pi/6)/2))
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= sqrt[(1-sqrt(3))/2)/2] = sqrt[(1-sqrt(3))/4]
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Cheers,
Stan H.
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