CAIE P3 2018 November — Question 4

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2018
SessionNovember
TopicParametric equations

4 The parametric equations of a curve are $$x = 2 \sin \theta + \sin 2 \theta , \quad y = 2 \cos \theta + \cos 2 \theta$$ where \(0 < \theta < \pi\).
  1. Obtain an expression for \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(\theta\).
  2. Hence find the exact coordinates of the point on the curve at which the tangent is parallel to the \(y\)-axis.