CAIE FP1 2008 June — Question 4

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2008
SessionJune
TopicPolar coordinates

4 The curves \(C _ { 1 }\) and \(C _ { 2 }\) have polar equations $$r = \theta + 2 \quad \text { and } \quad r = \theta ^ { 2 }$$ respectively, where \(0 \leqslant \theta \leqslant \pi\).
  1. Find the polar coordinates of the point of intersection of \(C _ { 1 }\) and \(C _ { 2 }\).
  2. Sketch \(C _ { 1 }\) and \(C _ { 2 }\) on the same diagram.
  3. Find the area bounded by \(C _ { 1 } , C _ { 2 }\) and the line \(\theta = 0\).