# Thread: Compound trig problem and general solutions

1. ## Compound trig problem and general solutions

Hi - Needs some pointers on this question as can't find any examples like it in any books.

Find the general solutions to:

$\displaystyle \cos \left(7\theta \right) = \cos \left( 9\theta - \frac \pi{7} \right )$

Not really sure where to start with this at all! I know the general solution formulas but need a push in the right direction. Do I use the sum and difference identities, or compound identities to get to the double angle ones.?? really not sure so your help would be great.

Thanks, Felix

2. ## Re: Compound trig problem and general solutions

In general, if $\displaystyle \cos(x)=\cos(a)$ then all the solutions are:
$\displaystyle x=\pm a + 2k\pi$

3. ## Re: Compound trig problem and general solutions

I know the general solution but how do I manipuate the equation to give me a principle value I can then work with?

4. ## Re: Compound trig problem and general solutions

Originally Posted by FelixHelix
I know the general solution but how do I manipuate the equation to give me a principle value I can then work with?
The principal value is the solution to $\displaystyle 7\theta = 9\theta - \dfrac{\pi}{7}$

5. ## Re: Compound trig problem and general solutions

I see. So after manipulating this I get:

$\displaystyle \theta = \pm \frac\pi{14} + n\pi$

$\displaystyle \left(n \in \mathbb{Z} \right)$

Could you confirm this?

6. ## Re: Compound trig problem and general solutions

Originally Posted by FelixHelix
I see. So after manipulating this I get:

$\displaystyle \theta = \pm \frac\pi{14} + n\pi$

$\displaystyle \left(n \in \mathbb{Z} \right)$

Could you confirm this?
Yep, you can also check in the original equation