Period and vertical shift of a sine model from its turning points, a second sine model through two points and their greatest difference

A function \(f\) is given by \(f(x)=3.6\sin{\left(\frac{\pi}{4}(x-0.6)\right)}+b\), for \(0\leq x\leq10\), where \(b\in\mathbb{R}\).

1. Write down the period of \(f\).[2]

The graph of \(f\) has a local maximum point at \((2.6,\ 12.1)\) and a local minimum point at \((6.6,\ 4.9)\).

2. 1. Find \(b\).
   2. Hence, find \(f(6)\).[4]

A function \(g\) is given by \(g(x)=p\sin{\left(\frac{\pi}{3}(x-4.5)\right)}+q\), for \(0\leq x\leq10\), where \(p,q\in\mathbb{R}\). The graph of \(g\) passes through the points \((5,\ 9.3)\) and \((9,\ -1.2)\).

3. Find the value of \(p\) and the value of \(q\).[5]
4. Find the value of \(x\), for \(0\leq x\leq10\), at which the difference between \(f(x)\) and \(g(x)\) is greatest.[2]