AQA C4 2009 January — Question 2

Exam BoardAQA
ModuleC4 (Core Mathematics 4)
Year2009
SessionJanuary
TopicHarmonic Form

2
  1. Express \(\sin x - 3 \cos x\) in the form \(R \sin ( x - \alpha )\), where \(R > 0\) and \(0 < \alpha < \frac { \pi } { 2 }\). Give your value of \(\alpha\) in radians to two decimal places.
  2. Hence:
    1. write down the minimum value of \(\sin x - 3 \cos x\);
    2. find the value of \(x\) in the interval \(0 < x < 2 \pi\) at which this minimum value occurs, giving your value of \(x\) in radians to two decimal places.