Edexcel P1 2021 June — Question 9

Exam BoardEdexcel
ModuleP1 (Pure Mathematics 1)
Year2021
SessionJune
TopicTrig Graphs & Exact Values

9. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{877d03f2-d62c-4060-bdd2-f0d5dfbe6203-30_707_1034_251_456} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} Figure 4 shows a sketch of the curve with equation $$y = \tan x \quad - 2 \pi \leqslant x \leqslant 2 \pi$$ The line \(l\), shown in Figure 4, is an asymptote to \(y = \tan x\)
  1. State an equation for \(l\). A copy of Figure 4, labelled Diagram 1, is shown on the next page.
    1. On Diagram 1, sketch the curve with equation $$y = \frac { 1 } { x } + 1 \quad - 2 \pi \leqslant x \leqslant 2 \pi$$ stating the equation of the horizontal asymptote of this curve.
    2. Hence, giving a reason, state the number of solutions of the equation
  2. State the number of solutions of the equation \(\tan x = \frac { 1 } { x } + 1\) in the region
    1. \(0 \leqslant x \leqslant 40 \pi\)
    2. \(- 10 \pi \leqslant x \leqslant \frac { 5 } { 2 } \pi\) $$\begin{aligned} & \qquad \tan x = \frac { 1 } { x } + 1
      & \text { in the region } - 2 \pi \leqslant x \leqslant 2 \pi \end{aligned}$$" \begin{figure}[h]
      \includegraphics[alt={},max width=\textwidth]{877d03f2-d62c-4060-bdd2-f0d5dfbe6203-31_725_1047_1078_447} \captionsetup{labelformat=empty} \caption{Diagram 1}
      \end{figure}
      \includegraphics[max width=\textwidth, alt={}]{877d03f2-d62c-4060-bdd2-f0d5dfbe6203-32_2644_1837_118_114}