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trigonometry

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Find all the angles between 0 degrees and 360 degrees which will satisf y the equation:
5tan^2 y +5 tan y = 2 sec^2 y

  • trigonometry -

    recalling that sec^2 = 1+tan^2, rearrange things to have

    3tan^2 y + 5 tan y - 2 = 0
    (3tan y - 1)(tan y + 2) = 0

    tan y = 1/3 or -2

    tan is positive in QI and QIII, so tany = 1/3 means that
    y = 18.43° or 198.43°

    tany = -2 means
    y = 116.57° or 296.57°

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