SOLUTION: Solve the given equation in the interval [0,2pi]. The answer must be written as a multiple of pi. Give exact answers. Do not use decimal numbers. The answer must be an integer or

Algebra ->  Trigonometry-basics -> SOLUTION: Solve the given equation in the interval [0,2pi]. The answer must be written as a multiple of pi. Give exact answers. Do not use decimal numbers. The answer must be an integer or      Log On


   



Question 928623: Solve the given equation in the interval [0,2pi].
The answer must be written as a multiple of pi. Give exact answers. Do not use decimal numbers. The answer must be an integer or a fraction.
2 (sin x)^2-5 cos x - 4 = 0.
Help would be appreciated dearly.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
2 (sin x)^2-5 cos x - 4 = 0.
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2(1-cos^2)-5cos - 4 = 0
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2 - 2cos^2 - 5cos - 4 = 0
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2cos^2 + 5cos +2 = 0
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Factor::
(2cos+1)(cos+2) = 0
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cos(x) = -1/2 or cos(x) = -2
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cos(x) = -2 implies x = (2/3)pi or (4/3)pi
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cos(x) = -2 is extraneous
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Cheers,
Stan H.
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