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Advanced Functions

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Determine all solutions in the interval
x is all real numbers , [0, 2 pi]
using a trigonometric identify

2cos^2x + sinx - 1 = 0

  • Advanced Functions - ,

    2cos^2x + sinx - 1 = 0
    2(1 - sin^2x) + sinx - 1 = 0
    2 - 2sin^2x + sinx - 1 = -
    2sin^2x - sinx -1 = 0
    (2sinx + 1)(sinx - 1) = 0
    sinx = -1/2 or sinx = 1

    from sinx = -1/2, x = pi + pi/6 or 2pi - pi/6
    x = 7pi/6 radians or 11pi/6 radians ,
    (210º or 330º)

    from sinx = 1, x = pi/4 radians, (90º)

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