- (a) Express \(3 \sin x + 2 \cos x\) in the form \(R \sin ( x + \alpha )\) where \(R > 0\) and \(0 < \alpha < \frac { \pi } { 2 }\).
(b) Hence find the greatest value of \(( 3 \sin x + 2 \cos x ) ^ { 4 }\).
(c) Solve, for \(0 < x < 2 \pi\), the equation
$$3 \sin x + 2 \cos x = 1$$
giving your answers to 3 decimal places.