Answer: \(a=4\), \(b=\frac38\), \(c=-2\).

For a trigonometric graph, identify the amplitude, midline and period first, then use these to locate the key points of the sketch.

The maximum value of the graph is \(2\) and the minimum value is \(-6\). Therefore the amplitude is

\(\frac{2-(-6)}{2}=4,\)

so \(a=4\).

The midline is

\(\frac{2+(-6)}{2}=-2,\)

so \(c=-2\).

The graph has a maximum at \(x=0^\circ\) and a minimum at \(x=480^\circ\), so \(480^\circ\) is half a period. Therefore the full period is \(960^\circ\).

For \(y=a\cos bx+c\), the period is \(\frac{360^\circ}{b}\). Hence

\(\frac{360}{b}=960.\)

So

\(b=\frac{360}{960}=\frac38.\)