Trigonometry - Trigonometric Graphs and Parameters

The curve, \(y = a \cos \left(\frac{x}{b}\right) + c\) is defined for \(0^\circ \leq x \leq 720^\circ\), where \(a\) and \(b\) are positive integers.

Given that the amplitude of \(y\) is \(5\) and that the period of \(y\) is \(720^\circ\).

1. State the value of \(a\) and of \(b\).
2. Given that the minimum value of \(y\) is \(-7\), state the value of \(c\).
3. Sketch the graph of \(y\), indicating clearly the coordinates of any maximum or minimum points on the graph.
4. State the range of values of \(k\) for which the equation \(a \cos \left(\frac{x}{b}\right) + c = k\) has \(2\) unique solutions.