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solve 0=(3^0.5)tan(x+(pi/6))+1 and find all general solutions

  • math - ,

    (3^0.5)tan(x+(pi/6))+1 = 0
    I am going to let x=pi/6 = y for easier typing

    (3^0.5)tan(y)+1 = 0

    tany = -1/√3 ...... ah!, tan 30º = +1/√3

    so y must be in the second or fourth quadrants.
    y = 150º or y = 330º or (5pi/6, 11pi/6)


    then x+pi/6 = 5pi/6
    x = 2pi/3
    or
    x+pi/6 = 11pi/6
    x = 5pi/3

    the period of your function is pi

    so the general solutions:
    x = 2pi/3 + kpi or
    x = 5pi/3 + kpi , where k is an integer.

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