CAIE P1 2013 June — Question 5

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2013
SessionJune
TopicHarmonic Form

5 It is given that \(a = \sin \theta - 3 \cos \theta\) and \(b = 3 \sin \theta + \cos \theta\), where \(0 ^ { \circ } \leqslant \theta \leqslant 360 ^ { \circ }\).
  1. Show that \(a ^ { 2 } + b ^ { 2 }\) has a constant value for all values of \(\theta\).
  2. Find the values of \(\theta\) for which \(2 a = b\).