Express \(2 \cos x - 5 \sin x\) in the form \(R \cos ( x + \alpha )\), where \(R > 0\) and \(0 < \alpha < \frac { \pi } { 2 }\), giving your value of \(\alpha\), in radians, to three significant figures.
Hence find the value of \(x\) in the interval \(0 < x < 2 \pi\) for which \(2 \cos x - 5 \sin x\) has its maximum value. Give your value of \(x\) to three significant figures.
Use your answer to part (a) to solve the equation \(2 \cos x - 5 \sin x + 1 = 0\) in the interval \(0 < x < 2 \pi\), giving your solutions to three significant figures. [0pt]
[3 marks]