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Math Help - General solution to a trig equation by turning it into a polynomial equation

  1. #1
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    General solution to a trig equation by turning it into a polynomial equation

    by putting t = tan\frac{\theta}{2}, find the general solution of the equation

    3cos\theta + 4sin\theta = 3 - tan\frac{\theta}{2}


    OK i've worked it out to

    t(t-3)(t-3)

    \therefore t=0, t=3

    but not sure what to do from here.

    I also know the general solution for tan is \theta=\pi n + \alpha
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  2. #2
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    Quote Originally Posted by djmccabie View Post
    by putting t = tan\frac{\theta}{2}, find the general solution of the equation

    3cos\theta + 4sin\theta = 3 - tan\frac{\theta}{2}


    OK i've worked it out to

    t(t-3)(t-3)

    \therefore t=0, t=3

    but not sure what to do from here.

    I also know the general solution for tan is \theta=\pi n + \alpha
    If t= tan(\frac{\theta}{2})= 0 or t= tan(\frac{\theta}{2})= 3, what are the possible values of \theta?
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  3. #3
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    Well i have done

    arctan (0) =0

    and

    arctan(3) = 1.249045772 (When calculator set to radians)

    but it's not really what i was expecting to see :/ doesn't look right??
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