Answer: \(a=2,\ b=3,\ c=-4\).

Answer: \(a=2,\ b=3,\ c=-4\).

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

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

so

\(c=-4.\)

The amplitude is

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

so

\(a=2.\)

The distance between two consecutive maxima is

\(\frac{2\pi}{3}.\)

For \(y=a\sin bx+c\), the period is \(\frac{2\pi}{b}\). Hence

\(\frac{2\pi}{b}=\frac{2\pi}{3},\)

so

\(b=3.\)