CAIE P3 2011 June — Question 5

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2011
SessionJune
TopicParametric equations

5 The parametric equations of a curve are $$x = \ln ( \tan t ) , \quad y = \sin ^ { 2 } t$$ where \(0 < t < \frac { 1 } { 2 } \pi\).
  1. Express \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(t\).
  2. Find the equation of the tangent to the curve at the point where \(x = 0\).