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 \(\theta = 0\).

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 $\theta = 0$.

\hfill \mbox{\textit{CAIE FP1 2015 Q5}}