Express \(3 \sin x - 4 \cos x\) in the form \(R \sin ( x - \alpha )\), where \(R > 0\) and \(0 ^ { \circ } < \alpha < 90 ^ { \circ }\). Give the value of \(\alpha\) correct to \(\mathbf { 4 }\) significant figures.
Hence solve the equation \(3 \sin x - 4 \cos x = 2\) for \(0 ^ { \circ } < x < 90 ^ { \circ }\), giving your answer correct to 3 significant figures.