Edexcel C3 2014 January — Question 5

Exam BoardEdexcel
ModuleC3 (Core Mathematics 3)
Year2014
SessionJanuary
TopicHarmonic Form

5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6f22eb1b-21de-45f1-9a8a-deac7ac8d0b0-14_646_1013_207_532} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} The curve shown in Figure 1 has equation $$x = 3 \sin y + 3 \cos y , \quad - \frac { \pi } { 4 } < y < \frac { \pi } { 4 }$$
  1. Express the equation of the curve in the form
    \(x = R \sin ( y + \alpha )\), where \(R\) and \(\alpha\) are constants, \(R > 0\) and \(0 < \alpha < \frac { \pi } { 2 }\)
  2. Find the coordinates of the point on the curve where the value of \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) is \(\frac { 1 } { 2 }\). Give your answers to 3 decimal places.