Edexcel P1 2023 October — Question 10

Exam BoardEdexcel
ModuleP1 (Pure Mathematics 1)
Year2023
SessionOctober
TopicTrig Graphs & Exact Values

10. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c0b4165d-b8bb-419c-b75a-d6c0c2431510-28_538_652_255_708} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} Figure 4 shows a sketch of part of the curve \(C _ { 1 }\) with equation $$y = 3 \cos \left( \frac { x } { n } \right) ^ { \circ } \quad x \geqslant 0$$ where \(n\) is a constant.
The curve \(C _ { 1 }\) cuts the positive \(x\)-axis for the first time at point \(P ( 270,0 )\), as shown in Figure 4.
    1. State the value of \(n\)
    2. State the period of \(C _ { 1 }\) The point \(Q\), shown in Figure 4, is a minimum point of \(C _ { 1 }\)
  1. State the coordinates of \(Q\). The curve \(C _ { 2 }\) has equation \(y = 2 \sin x ^ { \circ } + k\), where \(k\) is a constant.
    The point \(R \left( a , \frac { 12 } { 5 } \right)\) and the point \(S \left( - a , - \frac { 3 } { 5 } \right)\), both lie on \(C _ { 2 }\)
    Given that \(a\) is a constant less than 90
  2. find the value of \(k\).