AQA C4 2006 January — Question 3

Exam BoardAQA
ModuleC4 (Core Mathematics 4)
Year2006
SessionJanuary
TopicAddition & Double Angle Formulae

3 It is given that \(3 \cos \theta - 2 \sin \theta = R \cos ( \theta + \alpha )\), where \(R > 0\) and \(0 ^ { \circ } < \alpha < 90 ^ { \circ }\).
  1. Find the value of \(R\).
  2. Show that \(\alpha \approx 33.7 ^ { \circ }\).
  3. Hence write down the maximum value of \(3 \cos \theta - 2 \sin \theta\) and find a positive value of \(\theta\) at which this maximum value occurs.