Edexcel C4 2006 June — Question 4

Exam BoardEdexcel
ModuleC4 (Core Mathematics 4)
Year2006
SessionJune
TopicParametric equations

4. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 2} \includegraphics[alt={},max width=\textwidth]{c0c6303b-f527-4e68-91bc-5c9c6ffa8de8-05_480_1059_313_438}
\end{figure} The curve shown in Figure 2 has parametric equations $$x = \sin t , y = \sin \left( t + \frac { \pi } { 6 } \right) , \quad - \frac { \pi } { 2 } < t < \frac { \pi } { 2 }$$
  1. Find an equation of the tangent to the curve at the point where \(t = \frac { \pi } { 6 }\).
  2. Show that a cartesian equation of the curve is $$y = \frac { \sqrt { } 3 } { 2 } x + \frac { 1 } { 2 } \sqrt { } \left( 1 - x ^ { 2 } \right) , \quad - 1 < x < 1$$