(a)[5]
Express $f(\theta)$ as $R\cos(2\theta - \alpha) + k$, where $R > 0$, $0 < \alpha < \frac{\pi}{2}$ and $k$ is a constant. State the values of $R$ and $k$, and give $\alpha$ correct to $4$ significant figures.
(b)[3]
Find the least positive value of $\theta$ that satisfies the equation $f(\theta) = 17$.
(c)[2]
Find the integral $\int f(\theta)\, d\theta$.