(a)[3]
Write $7\cos\theta + 24\sin\theta$ in the form $R\cos(\theta - \alpha)$, with $R > 0$ and $0^\circ < \alpha < 90^\circ$. Give $\alpha$ correct to 2 decimal places.
(b)[4]
Solve $7\cos\theta + 24\sin\theta = 18$ for $0^\circ < \theta < 360^\circ$.
(c)[4]
As $\beta$ changes, the largest possible value of $\dfrac{150}{7\cos\left(\tfrac{1}{2}\beta\right) + 24\sin\left(\tfrac{1}{2}\beta\right) + 50}$ is denoted by $V$. Find $V$ and the smallest positive value of $\beta$ (in degrees) for which $V$ is obtained.