# Algebra STEP III Q4

I don't understand how I was meant to know the format the answer was wanted in. The official solutions give theta in terms of a and b. But I don't understand why the question didn't specifically ask for that

Are you talking about question 2? If $a$ and $b$ are in the original equation, it's not really surprising that they'd also be in the answer. What form did you give your answer in?

### Ah yes sorry

Ah yes sorry. Q2. The final answers were given theta = f(a, b) but the question doesn't specifically ask for that so I just left them in the form f(a, b, theta) = 2(pi)n or similar

### You'd definitely get most of

You'd definitely get most of the marks for that but, because you haven't removed the spurious solutions $\theta=2m\pi, \; m\in \mathbb{Z}$, you might lose a mark or two. If you did leave your answers in the form: $$\frac{1}{2}(b-a)\theta=n\pi,\quad \frac{1}{2}(b+a-1)\theta=\frac{1}{2}(2m+1)\pi,\quad n,m \in \mathbb{Z},\quad\frac{n}{b-a}\notin \mathbb{Z}$$ (i.e. you removed the spurious solutions), then I don't think you would have lost any marks.

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