Edexcel C4 Specimen — Question 4

Exam BoardEdexcel
ModuleC4 (Core Mathematics 4)
SessionSpecimen
TopicParametric equations

4. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 1} \includegraphics[alt={},max width=\textwidth]{0191bf56-a59e-44fe-af8c-bad796156f63-3_458_1552_415_223}
\end{figure} Figure 1 shows part of the curve with parametric equations $$x = \tan t , \quad y = \sin 2 t , \quad - \frac { \pi } { 2 } < t < \frac { \pi } { 2 } .$$
  1. Find the gradient of the curve at the point \(P\) where \(t = \frac { \pi } { 3 }\).
  2. Find an equation of the normal to the curve at \(P\).
  3. Find an equation of the normal to the curve at the point \(Q\) where \(t = \frac { \pi } { 4 }\).