CAIE FP1 2014 June — Question 5

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2014
SessionJune
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPolar coordinates

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}}