2 The equation of the curve shown on the graph is, in polar coordinates, \(r = 3 \sin 2 \theta\) for \(0 \leqslant \theta \leqslant \frac { 1 } { 2 } \pi\).
\includegraphics[max width=\textwidth, alt={}, center]{8315a796-0e7d-464f-8604-9fe3ab7af359-2_470_657_913_319}
- The greatest value of \(r\) on the curve occurs at the point \(P\).
- Show that \(\theta = \frac { 1 } { 4 } \pi\) at the point \(P\).
- Find the value of \(r\) at the point \(P\).
- Mark the point \(P\) on the copy of the graph in the Printed Answer Booklet.
- In this question you must show detailed reasoning.
Find the exact area of the region enclosed by the curve.