Express \(2 \sin x + 5 \cos x\) in the form \(R \sin ( x + \alpha )\), where \(R > 0\) and \(0 ^ { \circ } < \alpha < 90 ^ { \circ }\). Give your value of \(\alpha\) to the nearest \(0.1 ^ { \circ }\).
Write down the maximum value of \(2 \sin x + 5 \cos x\).
Find the value of \(x\) in the interval \(0 ^ { \circ } \leqslant x \leqslant 360 ^ { \circ }\) at which this maximum occurs, giving the value of \(x\) to the nearest \(0.1 ^ { \circ }\).