Answer: amplitude \(3\), period \(180^\circ\).

The graph is

\(y=3\cos 2x-1.\)

The coefficient of the cosine term is \(3\), so the amplitude is

\(3\).

For \(\cos bx\), when angles are measured in degrees, the period is \(\dfrac{360^\circ}{b}\). Here \(b=2\), so the period is

\(\dfrac{360^\circ}{2}=180^\circ.\)

The vertical translation is \(-1\), so the midline of the graph is \(y=-1\). Since the amplitude is \(3\), the maximum value is

\(-1+3=2,\)

and the minimum value is

\(-1-3=-4.\)

For the sketch, use one full cycle every \(180^\circ\). The important points in \(0^\circ\leqslant x\leqslant360^\circ\) are

\((0^\circ,2),\ (45^\circ,-1),\ (90^\circ,-4),\ (135^\circ,-1),\ (180^\circ,2),\)

and then the same pattern repeats:

\((225^\circ,-1),\ (270^\circ,-4),\ (315^\circ,-1),\ (360^\circ,2).\)

Therefore the amplitude is \(3\), and the period is \(180^\circ\).