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Trigonometry

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Use inverse trigonometric functions to find the solutions of the equation that are in the given interval, and approximate the solutions to four decimal places. (Enter your answers as a comma-separated list.)
cos(x)(9cos(x) + 4) = 4; [0, 2π)

  • Trigonometry - ,

    expand first
    9cos^2 x + 4cosx - 4 = 0
    let y = cosx
    9y^2 + 4y - 4 = 0
    y = (-4 ±√160)/18 , using the formula
    = (-4 + 4√10)/18
    = (-2 ± 2√10)/9
    = appr .480506 or appr -.92495

    then cosx = .480506 or cosx = -.92495
    x = 61.28° or 298.72° or 157.66° or 202.34°

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