Edexcel P4 2018 Specimen — Question 4

Exam BoardEdexcel
ModuleP4 (Pure Mathematics 4)
Year2018
SessionSpecimen
TopicParametric equations

4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4de08317-5fb9-4789-8d57-ccf463224c78-10_899_759_127_621} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a sketch of the curve \(C\) with parametric equations $$x = \sqrt { 3 } \sin 2 t \quad y = 4 \cos ^ { 2 } t \quad 0 \leqslant t \leqslant \pi$$
  1. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = k \sqrt { 3 } \tan 2 t\), where \(k\) is a constant to be found.
  2. Find an equation of the tangent to \(C\) at the point where \(t = \frac { \pi } { 3 }\) Give your answer in the form \(y = a x + b\), where \(a\) and \(b\) are constants.