5 The curve \(C\) has polar equation \(r = 3 + 2 \sin \theta\), for \(- \pi < \theta \leqslant \pi\).
- The diagram shows part of \(C\). Sketch the rest of \(C\) on the diagram.
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The straight line \(l\) has polar equation \(r \sin \theta = 2\). - Add \(l\) to the diagram in part (a) and find the polar coordinates of the points of intersection of \(C\) and \(l\).
- The region \(R\) is enclosed by \(C\) and \(l\), and contains the pole.
Find the area of \(R\), giving your answer in exact form.