Edexcel P1 2019 October — Question 9

Exam BoardEdexcel
ModuleP1 (Pure Mathematics 1)
Year2019
SessionOctober
TopicTrig Graphs & Exact Values

9. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{50ec901b-b6b6-4b72-85bd-a084f313c99b-20_671_856_303_548} \captionsetup{labelformat=empty} \caption{Figure 5}
\end{figure} Figure 5 shows a sketch of part of the curve \(C\) with equation \(y = \sin \left( \frac { x } { 12 } \right)\), where \(x\) is measured in radians. The point \(M\) shown in Figure 5 is a minimum point on \(C\).
  1. State the period of \(C\).
  2. State the coordinates of \(M\). The smallest positive solution of the equation \(\sin \left( \frac { x } { 12 } \right) = k\), where \(k\) is a constant, is \(\alpha\). Find, in terms of \(\alpha\),
    1. the negative solution of the equation \(\sin \left( \frac { x } { 12 } \right) = k\) that is closest to zero,
    2. the smallest positive solution of the equation \(\cos \left( \frac { x } { 12 } \right) = k\).