CAIE P3 2019 June — Question 7

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2019
SessionJune
TopicDifferentiating Transcendental Functions

7 The curve \(y = \sin \left( x + \frac { 1 } { 3 } \pi \right) \cos x\) has two stationary points in the interval \(0 \leqslant x \leqslant \pi\).
  1. Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
  2. By considering the formula for \(\cos ( A + B )\), show that, at the stationary points on the curve, \(\cos \left( 2 x + \frac { 1 } { 3 } \pi \right) = 0\).
  3. Hence find the exact \(x\)-coordinates of the stationary points.