CAIE P3 2021 November — Question 2

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2021
SessionNovember
TopicHarmonic Form

2
  1. Express \(5 \sin x - 3 \cos x\) in the form \(R \sin ( x - \alpha )\), where \(R > 0\) and \(0 < \alpha < \frac { 1 } { 2 } \pi\). Give the exact value of \(R\) and give \(\alpha\) correct to 2 decimal places.
  2. Hence state the greatest and least possible values of \(( 5 \sin x - 3 \cos x ) ^ { 2 }\).