Answer: \(a=5\), \(b=4\), \(c=-3\).

Answer: \(a=5\), \(b=4\), \(c=-3\).

From the graph, the maximum value is \(2\) and the minimum value is \(-8\).

The amplitude is

\(\frac{2-(-8)}{2}=5,\)

so \(a=5\).

The midline is

\(\frac{2+(-8)}{2}=-3,\)

so \(c=-3\).

The graph completes one cycle every \(90^{\circ}\). For \(y=a\sin bx+c\), the period is \(\frac{360^{\circ}}{b}\). Hence

\(\frac{360^{\circ}}{b}=90^{\circ},\)

so \(b=4\).