OCR MEI C4 2012 January — Question 3

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Year2012
SessionJanuary
TopicHarmonic Form

3 Express \(3 \sin x + 2 \cos x\) in the form \(R \sin ( x + \alpha )\), where \(R > 0\) and \(0 < \alpha < \frac { \pi } { 2 }\).
Hence find, correct to 2 decimal places, the coordinates of the maximum point on the curve \(y = \mathrm { f } ( x )\), where $$f ( x ) = 3 \sin x + 2 \cos x , 0 \leqslant x \leqslant \pi .$$