9 A curve has polar equation \(r = \operatorname { asin } 3 \theta\), for \(0 \leqslant \theta \leqslant \pi\), where \(a\) is a positive constant.
- Sketch the curve. Indicate the parts of the curve where \(r\) is negative by using a broken line.
- In this question you must show detailed reasoning.
Determine the area of one of the loops of the curve.