SOLUTION: The equation contains the measure of 2 acute angles. Find a value of �for which this statement is true. Sin x=cos 2�

Question 792524: The equation contains the measure of 2 acute angles. Find a value of �for which this statement is true. Sin x=cos 2�
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Sin x=cos (2x)
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sinx = cos^2(x)-sin^2(x)
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sin(x) = 1-2sin^2(x)
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2sin^2(x) + sin(x) - 1 = 0
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sin(x) = [1 +- sqrt(1-4*-1)]/2
sin(x) = [1+-sqrt(5)]/2
sin(x) = (1/2)+(1/2)sqrt(5) or sin(x) = (1/2)-(1/2)sqrt(5)
Only sin(x) = (1-sqrt(5))/2 has solutions.
sin(x) = -0.6180
x = sin^-1(-0.6180) = -38.17 degrees or x = 180+38.17 = 28.17
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Cheers,
Stan H.
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