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

• May 18th 2009, 12:31 PM
djmccabie
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 $\displaystyle \theta=\pi n + \alpha$
• May 18th 2009, 12:49 PM
HallsofIvy
Quote:

Originally Posted by djmccabie
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 $\displaystyle \theta$?
• May 18th 2009, 12:51 PM
djmccabie
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??