Edexcel C4 2009 June — Question 5

Exam BoardEdexcel
ModuleC4 (Core Mathematics 4)
Year2009
SessionJune
TopicParametric equations

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 $$x = 2 \cos 2 t , \quad y = 6 \sin t , \quad 0 \leqslant t \leqslant \frac { \pi } { 2 }$$
  1. Find the gradient of the curve at the point where \(t = \frac { \pi } { 3 }\).
  2. 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 \(k\).
  3. Write down the range of \(\mathrm { f } ( x )\).