CAIE P2 2003 June — Question 7

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2003
SessionJune
TopicParametric equations

7 The parametric equations of a curve are $$x = 2 \theta - \sin 2 \theta , \quad y = 2 - \cos 2 \theta$$
  1. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \cot \theta\).
  2. Find the equation of the tangent to the curve at the point where \(\theta = \frac { 1 } { 4 } \pi\).
  3. For the part of the curve where \(0 < \theta < 2 \pi\), find the coordinates of the points where the tangent is parallel to the \(x\)-axis.