7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{7c3dd501-0545-4166-aaf9-5e1ac1f369c5-4_552_771_248_470}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows the curve \(y = \mathrm { f } ( x )\) which has a maximum point at ( \(- 45,7\) ) and a minimum point at \(( 135 , - 1 )\).
- Showing the coordinates of any stationary points, sketch on separate diagrams the graphs of
- \(y = \mathrm { f } ( | x | )\),
- \(y = 1 + 2 \mathrm { f } ( x )\).
Given that
$$f ( x ) = A + 2 \sqrt { 2 } \cos x ^ { \circ } - 2 \sqrt { 2 } \sin x ^ { \circ } , \quad x \in \mathbb { R } , \quad - 180 \leq x \leq 180 ,$$
where \(A\) is a constant,
- show that \(\mathrm { f } ( x )\) can be expressed in the form
$$\mathrm { f } ( x ) = A + R \cos ( x + \alpha ) ^ { \circ } ,$$
where \(R > 0\) and \(0 < \alpha < 90\),
- state the value of \(A\),
- find, to 1 decimal place, the \(x\)-coordinates of the points where the curve \(y = \mathrm { f } ( x )\) crosses the \(x\)-axis.