Express \(\cos x + 3 \sin x\) in the form \(R \cos ( x - \alpha )\), where \(R > 0\) and \(0 < \alpha < \frac { \pi } { 2 }\). Give your value of \(\alpha\), in radians, to three decimal places.
Hence write down the minimum value of \(\cos x + 3 \sin x\).
Find the value of \(x\) in the interval \(0 \leqslant x \leqslant 2 \pi\) at which this minimum occurs, giving your answer, in radians, to three decimal places.
Solve the equation \(\cos x + 3 \sin x = 2\) in the interval \(0 \leqslant x \leqslant 2 \pi\), giving all solutions, in radians, to three decimal places.