AQA FP3 2009 January — Question 3

Exam BoardAQA
ModuleFP3 (Further Pure Mathematics 3)
Year2009
SessionJanuary
TopicPolar 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.