Express \(4 \cos x + 3 \sin x\) in the form \(R \cos ( x - \alpha )\), where \(R > 0\) and \(0 ^ { \circ } < \alpha < 360 ^ { \circ }\), giving your value for \(\alpha\) to the nearest \(0.1 ^ { \circ }\).
Hence solve the equation \(4 \cos x + 3 \sin x = 2\) in the interval \(0 ^ { \circ } < x < 360 ^ { \circ }\), giving all solutions to the nearest \(0.1 ^ { \circ }\).
Write down the minimum value of \(4 \cos x + 3 \sin x\) and find the value of \(x\) in the interval \(0 ^ { \circ } < x < 360 ^ { \circ }\) at which this minimum value occurs.