| Exam Board | CAIE |
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2015 |
| Session | June |
| Topic | Polar coordinates |
5 The curves \(C _ { 1 }\) and \(C _ { 2 }\) have polar equations
$$\begin{array} { l l }
C _ { 1 } : & r = \frac { 1 } { \sqrt { 2 } } , \quad \text { for } 0 \leqslant \theta < 2 \pi
C _ { 2 } : & r = \sqrt { } \left( \sin \frac { 1 } { 2 } \theta \right) , \quad \text { for } 0 \leqslant \theta \leqslant \pi
\end{array}$$
Find the polar coordinates of the point of intersection of \(C _ { 1 }\) and \(C _ { 2 }\).
Sketch \(C _ { 1 }\) and \(C _ { 2 }\) on the same diagram.
Find the exact value of the area of the region enclosed by \(C _ { 1 } , C _ { 2 }\) and the half-line \(\theta = 0\).