CAIE P2 2018 June — Question 5

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2018
SessionJune
TopicParametric equations

5 The parametric equations of a curve are $$x = 2 \cos 2 \theta + 3 \sin \theta , \quad y = 3 \cos \theta$$ for \(0 < \theta < \frac { 1 } { 2 } \pi\).
  1. Find the gradient of the curve at the point for which \(\theta = 1\) radian.
  2. Find the value of \(\sin \theta\) at the point on the curve where the tangent is parallel to the \(y\)-axis.