OCR C4 2016 June — Question 9

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
Year2016
SessionJune
TopicParametric equations

9 A curve has parametric equations \(x = 1 - \cos t , y = \sin t \sin 2 t\), for \(0 \leqslant t \leqslant \pi\).
  1. Find the coordinates of the points where the curve meets the \(x\)-axis.
  2. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 2 \cos 2 t + 2 \cos ^ { 2 } t\). Hence find, in an exact form, the coordinates of the stationary points.
  3. Find the cartesian equation of the curve. Give your answer in the form \(y = \mathrm { f } ( x )\), where \(\mathrm { f } ( x )\) is a polynomial.
  4. Sketch the curve.