7.
\includegraphics[max width=\textwidth, alt={}, center]{6cdbc2bc-8863-4003-a218-44552d75d137-2_556_777_246_468}
The diagram 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 the curve with equation \(y = 1 + 2 \mathrm { f } ( x )\).
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.