Answer: period \(1080^\circ\); \(a=4\), \(b=3\), \(c=-2\).

The key point is to identify the important features of the graph before using it to answer the question.

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

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

so \(c=-2\). The amplitude is

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

so \(a=4\).

The graph goes from a minimum at \(x=-270^\circ\) to a maximum at \(x=270^\circ\). This is half a period, so the period is

\(2(270-(-270))=1080^\circ.\)

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

\(360b=1080,\)

so \(b=3\).