CAIE P3 2014 November — Question 4

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2014
SessionNovember
TopicParametric equations

4 The parametric equations of a curve are $$x = \frac { 1 } { \cos ^ { 3 } t } , \quad y = \tan ^ { 3 } t$$ where \(0 \leqslant t < \frac { 1 } { 2 } \pi\).
  1. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \sin t\).
  2. Hence show that the equation of the tangent to the curve at the point with parameter \(t\) is \(y = x \sin t - \tan t\).