Answer: The graph is a cosine curve with midline \(y=2\), maxima \(6\), minima \(-2\), two complete cycles on \(0^\circ\leq x\leq120^\circ\). The amplitude is \(4\) and the period is \(60^\circ\).

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

(a) The graph of \(g(x)=2+4\cos6x\) has midline

\(y=2.\)

Its maximum value is

\(2+4=6,\)

and its minimum value is

\(2-4=-2.\)

Since \(\cos6x\) has period

\(\frac{360^\circ}{6}=60^\circ,\)

the graph completes two cycles from \(0^\circ\) to \(120^\circ\). It has maxima at \(x=0^\circ,60^\circ,120^\circ\) and minima at \(x=30^\circ,90^\circ\).

(b) The amplitude is

\(4.\)

(c) The period is

\(60^\circ.\)

Therefore the result matches the required answer.