SPS SPS SM Pure 2024 June — Question 9

Exam BoardSPS
ModuleSPS SM Pure (SPS SM Pure)
Year2024
SessionJune
TopicTrig Graphs & Exact Values

9. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b063f4ea-372b-4193-b8fe-a9f8017d7349-18_718_882_219_596} \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 \(\tan x\)
      (1)
    2. Write down the number of roots of the equation
      1. \(\tan x = ( \pi + 2 ) x\) in the interval \(- \pi < x < \pi\)
        (1)
      2. \(\tan x = \pi x\) in the interval \(- 2 \pi < x < 2 \pi\)
        (1)
      3. \(\tan x = \pi x\) in the interval \(- 100 \pi < x < 100 \pi\)
        (1)