5 The curve \(C\) has polar equation \(r = a ( 1 + \sin \theta )\), where \(a\) is a positive constant and \(0 \leqslant \theta < 2 \pi\). Draw a sketch of \(C\).
Find the exact value of the area of the region enclosed by \(C\) and the half-lines \(\theta = \frac { 1 } { 3 } \pi\) and \(\theta = \frac { 2 } { 3 } \pi\).
5 The curve $C$ has polar equation $r = a ( 1 + \sin \theta )$, where $a$ is a positive constant and $0 \leqslant \theta < 2 \pi$. Draw a sketch of $C$.
Find the exact value of the area of the region enclosed by $C$ and the half-lines $\theta = \frac { 1 } { 3 } \pi$ and $\theta = \frac { 2 } { 3 } \pi$.
\hfill \mbox{\textit{CAIE FP1 2014 Q5}}