Edexcel P1 2023 January — Question 9

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

9. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bb21001f-fe68-4776-992d-ede1aae233d7-24_675_835_251_616} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Figure 3 shows a sketch of
  • the curve with equation \(y = \tan x\)
  • the straight line l with equation \(y = \pi x\)
    in the interval \(- \pi < x < \pi\)
    1. State the period of \(\tan x\)
    2. Write down the number of roots of the equation
      1. \(\tan x = ( \pi + 2 ) x\) in the interval \(- \pi < x < \pi\)
      2. \(\tan x = \pi x\) in the interval \(- 2 \pi < x < 2 \pi\)
      3. \(\tan x = \pi x\) in the interval \(- 100 \pi < x < 100 \pi\)