Kaitlyn V.
asked • 06/18/21Solve the equation for x if 0 ≤ x < 2𝜋. Give your answer in radians using exact values only. (Enter your answers as a comma-separated list.) 2 cos2 x + sin x − 1 = 0
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1 Expert Answer
Inactive Tutor answered • 06/18/21
Tutor
New to Wyzant
2cos^2x + sinx - 1 = 0
2(1-sin^2x) + sinx -1 = 0
-2sin^2x + sinx + 1 = 0
2sin^2x -sinx -1 = 0
(2sinx +1)(sinx-1) = 0
sinx = -1/2, 1
x = pi/2, 7pi/6, 11pi/6
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Inactive Tutor
It seems that the problem may be written incorrectly. Did you mean for the equation to be 2 cos^2(x) + sin(x) - 1 = 0? If it is in the form you wrote, then it would be quite difficult to find exact values. If it is in the form I indicated above, there are a couple of ways you can approach a problem like this. Are you having trouble conceptualizing the problem? Or is it more of the trigonometric identities/algebraic manipulation?06/18/21