CAIE FP1 2010 November — Question 8

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2010
SessionNovember
TopicPolar coordinates

8 The curves \(C _ { 1 }\) and \(C _ { 2 }\) have polar equations given by $$\begin{array} { l l r } C _ { 1 } : & r = 3 \sin \theta , & 0 \leqslant \theta < \pi ,
C _ { 2 } : & r = 1 + \sin \theta , & - \pi < \theta \leqslant \pi . \end{array}$$
  1. Find the polar coordinates of the points, other than the pole, where \(C _ { 1 }\) and \(C _ { 2 }\) meet.
  2. In a single diagram, draw sketch graphs of \(C _ { 1 }\) and \(C _ { 2 }\).
  3. Show that the area of the region which is inside \(C _ { 1 }\) but outside \(C _ { 2 }\) is \(\pi\).