Edexcel Paper 1 2019 June — Question 2

Exam BoardEdexcel
ModulePaper 1 (Paper 1)
Year2019
SessionJune
TopicSmall angle approximation

2. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{91a2f26a-add2-4b58-997d-2ae229548217-04_670_1447_212_333} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a plot of part of the curve with equation \(y = \cos x\) where \(x\) is measured in radians. Diagram 1, on the opposite page, is a copy of Figure 1.
  1. Use Diagram 1 to show why the equation $$\cos x - 2 x - \frac { 1 } { 2 } = 0$$ has only one real root, giving a reason for your answer. Given that the root of the equation is \(\alpha\), and that \(\alpha\) is small,
  2. use the small angle approximation for \(\cos x\) to estimate the value of \(\alpha\) to 3 decimal places.
    \includegraphics[max width=\textwidth, alt={}]{91a2f26a-add2-4b58-997d-2ae229548217-05_664_1452_246_333}
    \section*{Diagram 1}