Edexcel P1 2022 June — Question 9

Exam BoardEdexcel
ModuleP1 (Pure Mathematics 1)
Year2022
SessionJune
TopicTrig Graphs & Exact Values

9. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3cf69966-e825-4ff0-a6e8-c5dfdc92c53f-26_428_1354_251_287} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} Figure 4 shows part of the graph of the curve with equation \(y = \sin x\) Given that \(\sin \alpha = p\), where \(0 < \alpha < 90 ^ { \circ }\)
  1. state, in terms of \(p\), the value of
    1. \(2 \sin \left( 180 ^ { \circ } - \alpha \right)\)
    2. \(\sin \left( \alpha - 180 ^ { \circ } \right)\)
    3. \(3 + \sin \left( 180 ^ { \circ } + \alpha \right)\) A copy of Figure 4, labelled Diagram 1, is shown on page 27. On Diagram 1,
  2. sketch the graph of \(y = \sin 2 x\)
  3. Hence find, in terms of \(\alpha\), the \(x\) coordinates of any points in the interval \(0 < x < 180 ^ { \circ }\) where $$\sin 2 x = p$$
    \includegraphics[max width=\textwidth, alt={}]{3cf69966-e825-4ff0-a6e8-c5dfdc92c53f-27_433_1331_296_310}
    \section*{Diagram 1}