SOLUTION: Solve for all solutions, x, in degrees. {{{cos(2x)}}}={{{(1/2)cos(x)}}} Thank you!

Algebra ->  Trigonometry-basics -> SOLUTION: Solve for all solutions, x, in degrees. {{{cos(2x)}}}={{{(1/2)cos(x)}}} Thank you!      Log On


   

Question 1117819: Solve for all solutions, x, in degrees.
cos%282x%29=%281%2F2%29cos%28x%29



Thank you!
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for all solutions, x, in degrees.
cos(2x)=(1/2)cos(x)
2cos^2(x)-1 = (1/2)cos(x)
4cos^2(x)-2= cos(x)
4cos^2(x) - cos(x) - 2 = 0
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cos(x) = [1+-sqrt(1-4*4*-2)]/8
cos(x) = [1+-sqrt(33)]/8
cos(x) = 0.8431 or cos(x) = -0.5931
x = arccos(0.8431) = 32.53 degrees
Or
x = arccos(-0.5931) = 126.38 degrees
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Cheers,
Stan H.
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