5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c2622c33-9436-4254-a728-10ba4703a28c-09_735_1222_205_358}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows a sketch of the curve with parametric equations
$$x = 2 \cos 2 t , \quad y = 6 \sin t , \quad 0 \leqslant t \leqslant \frac { \pi } { 2 }$$
- Find the gradient of the curve at the point where \(t = \frac { \pi } { 3 }\).
- Find a cartesian equation of the curve in the form
$$y = \mathrm { f } ( x ) , \quad - k \leqslant x \leqslant k$$
stating the value of the constant \(k\).
- Write down the range of \(\mathrm { f } ( x )\).