Amplitude, period and cosine and sine models of a trigonometric graph from its turning points

The diagram below shows part of the graph of \(y=\mathrm{f}(x)\) for \(0\le x\le7.5\). The graph has a local maximum point at \(A(3,5)\) and a local minimum point at \(B(6,-1)\).

1. State, for the function \(\mathrm{f}\),[2]
   1. the amplitude;
   2. the period.
2. Find the values of the constants \(a\), \(b\) and \(c\) such that \(\mathrm{f}(x)=a\cos(bx)+c\), where \(b>0\).[4]
3. Hence, write \(\mathrm{f}(x)\) in the form \(p\sin(qx+r)+s\), where \(p>0\) and \(q>0\).[3]