Edexcel FP2 2013 June — Question 9

Exam BoardEdexcel
ModuleFP2 (Further Pure Mathematics 2)
Year2013
SessionJune
TopicPolar coordinates

9. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{1f8a7998-613b-449b-9758-9bf105c56a8f-9_370_820_316_626} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a sketch of the curves given by the polar equations $$r = 1 \text { and } r = 2 - 2 \sin \theta$$
  1. Find the coordinates of the points where the curves intersect. The region \(S\), between the curves, for which \(r < 1\) and for which \(r < 2 - 2 \sin \theta\), is shown shaded in Figure 1.
  2. Find, by integration, the area of the shaded region \(S\), giving your answer in the form \(a \pi + b \sqrt { } 3\), where \(a\) and \(b\) are rational numbers.