Question 866318: How many points in the interval 0 ≤ x ≤ 2π satisfy the equation cos 2x = –2 sin x?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! How many points in the interval 0 ≤ x ≤ 2π satisfy the equation cos 2x = –2 sin x?
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cos(2x) = -2sin(x)
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1-2sin^2(x) = -2sin(x)
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2sin^2(x) -2sin(x) - 1 = 0
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sin((x) = [2 +- sqrt(4-4*2*-1)]/4
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sin(x) = [2+-sqrt(12)]/4
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sin(x = [2[1+-sqrt(3)]/4
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sin(x) = (1/2)(1+sqrt(3)) or sin(x) = (1/2)(1-sqrt(3))
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Note:: (1/2)(1+sqrt(3) > 1 so no solutions there
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(1/2)(1-sqrt(3)) = -0.3660, so there are 2 solutions,
one in QIII, the other in QIV.
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Cheers,
Stan H.
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