- (a) Express \(7 \cos x - 24 \sin x\) in the form \(R \cos ( x + \alpha )\) where \(R > 0\) and \(0 < \alpha < \frac { \pi } { 2 }\). Give the value of \(\alpha\) to 3 decimal places.
(b) Hence write down the minimum value of \(7 \cos x - 24 \sin x\).
(c) Solve, for \(0 \leqslant x < 2 \pi\), the equation
$$7 \cos x - 24 \sin x = 10$$
giving your answers to 2 decimal places.