Express \(3 \cos x + 4 \sin x\) in the form \(R \cos ( x - \alpha )\), where \(R > 0\) and \(0 ^ { \circ } < \alpha < 90 ^ { \circ }\), stating the exact value of \(R\) and giving the value of \(\alpha\) correct to 2 decimal places.
Hence solve the equation
$$3 \cos x + 4 \sin x = 4.5$$
giving all solutions in the interval \(0 ^ { \circ } < x < 360 ^ { \circ }\).