C3 IYGB Trig question help

I'm doing Paper Q of the IYGB papers and am having trouble with question 8b.

The paper and mark scheme are here http://www.madasmaths.com/archive/iygb_practice_papers/c3_practice_papers/c3_q.pdf and http://www.madasmaths.com/archive/iygb_practice_papers/c3_practice_papers/c3_q_solutions.pdf

I get to the stage 2 theta - pi/3 = theta and then I can find the first solution, theta = pi/3. But after this I don't know how to find the other solutions.

Also, could a question like this be on an actual Edexcel C3 paper?

Thanks

Do you remember how to solve trig equations of the form $\cos x= k$?

We have that $x = \arccos k + 2n\pi$ but also (because fourth quadrant) .

I use the CAST diagram method.

After I had found theta = pi/3 I then wrote theta = 2pi - pi/3 to find the solution in the fourth quadrant.

This resulted in theta = 5pi/3 but this is not a correct solution.

You found $2\theta - \frac{\pi}{3} = \theta$ (the $\theta$ on your RHS is the "solution".

So you need to do: $2\theta - \frac{\pi}{3} = 2\pi - \theta$ now.

It might help for you to write $2\theta -\frac{\pi}{3} = x$ to help your visualisation.

Thanks I think I am starting to understand.

If this had been a typical C3 trig question (with theta on only 1 side of the equation), then my method would have worked. Why does it not work for this question?

Because $\theta$ is on both sides of the equation. You wouldn't get a question like that in an Edexcel exam though, or at least it would be very unlikely.

Okay thanks, I really hope it's not on the paper this year

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