- (i) Express \(4 \sin x + 3 \cos x\) in the form \(R \sin ( x + \alpha )\) where \(R > 0\) and \(0 < \alpha < \frac { \pi } { 2 }\).
(ii) State the minimum value of \(4 \sin x + 3 \cos x\) and the smallest positive value of \(x\) for which this minimum value occurs.
(iii) Solve the equation
$$4 \sin 2 \theta + 3 \cos 2 \theta = 2$$
for \(\theta\) in the interval \(0 \leq \theta \leq \pi\), giving your answers to 2 decimal places.