Trigonometry - Trigonometric Graphs and Parameters

The function \(\mathrm{f}\) is defined, for all values of \(x\), by \(\mathrm{f}\left( x \right)=a\sin x+b\), where \(a\) and \(b\) are constants. The graph of \(y=\mathrm{f}\left( x \right)\) passes through the point \(\left( 2\pi ,-1 \right)\) and the maximum value of \(y\) is \(4\).

1. Find the value of \(a\) and of \(b\) given that \(a < 0\).
2. State the amplitude and period of \(\mathrm{f}\) .
3. Sketch the graph of \(y=\mathrm{f}\left( x \right)\) for \(0\le x\le 2\pi \).