(a)[5]
Write $f(\theta)$ in the form $R \cos(2\theta - \alpha) + k$, where $R > 0$, $0 < \alpha < \frac{1}{2}\pi$ and $k$ is a constant. Give the values of $R$ and $k$, and state $\alpha$ correct to 4 significant figures.
(b)[3]
Find the least positive value of $\theta$ for which the equation $f(\theta) = 17$ is satisfied.
(c)[2]
Determine $\int f(\theta) \, d\theta$.