Answer: \(a=3,\ b=\dfrac12,\ c=4\).

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 \(7\), and the minimum value is \(1\). Therefore the amplitude is

\(a=\frac{7-1}{2}=3.\)

The midline is halfway between the maximum and minimum values:

\(c=\frac{7+1}{2}=4.\)

The graph crosses the midline at \(x=0\) and then reaches a maximum at \(x=\pi\). For \(y=a\sin bx+c\), a maximum occurs when

\(bx=\frac{\pi}{2}.\)

Using \(x=\pi\),

\(b\pi=\frac{\pi}{2},\)

so

\(b=\frac12.\)