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Thread: 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 $\displaystyle t = tan\frac{\theta}{2}$, find the general solution of the equation

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


    OK i've worked it out to

    $\displaystyle t(t-3)(t-3)$

    $\displaystyle \therefore t=0, t=3$

    but not sure what to do from here.

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

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


    OK i've worked it out to

    $\displaystyle t(t-3)(t-3)$

    $\displaystyle \therefore t=0, t=3$

    but not sure what to do from here.

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

    $\displaystyle arctan (0) =0$

    and

    $\displaystyle arctan(3) = 1.249045772$ (When calculator set to radians)

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