| Exam Board | AQA |
| Module | FP3 (Further Pure Mathematics 3) |
| Year | 2009 |
| Session | January |
| Topic | Polar coordinates |
3 The diagram shows a sketch of a loop, the pole \(O\) and the initial line.
\includegraphics[max width=\textwidth, alt={}, center]{f4fdffc7-5647-4462-a983-1564d4e76a4d-3_305_553_383_740}
The polar equation of the loop is
$$r = ( 2 + \cos \theta ) \sqrt { \sin \theta } , \quad 0 \leqslant \theta \leqslant \pi$$
Find the area enclosed by the loop.