4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3bd9d8a3-a324-4649-9357-392a48a4a1de-3_508_771_255_488}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows the graph of \(y = \mathrm { f } ( x )\). The graph has a minimum at \(\left( \frac { \pi } { 2 } , - 1 \right)\), a maximum at \(\left( \frac { 3 \pi } { 2 } , - 5 \right)\) and an asymptote with equation \(x = \pi\).
- Showing the coordinates of any stationary points, sketch the graph of \(y = | \mathrm { f } ( x ) |\).
Given that
$$f : x \rightarrow a + b \operatorname { cosec } x , \quad x \in \mathbb { R } , \quad 0 < x < 2 \pi , \quad x \neq \pi ,$$
- find the values of the constants \(a\) and \(b\),
- find, to 2 decimal places, the \(x\)-coordinates of the points where the graph of \(y = \mathrm { f } ( x )\) crosses the \(x\)-axis.