Parameters of a cosine function read from its graph, an equivalent sine form and an equation

The diagram shows the graph of \(y=f(x)\), where \(f(x)=a\cos(bx)+c\) for \(-4\le x\le10\) and \(b>0\). The graph has a maximum point at \((0,5)\), and the nearest minimum point to the right of it is \((3,-1)\).

1. Find the values of \(a\), \(b\) and \(c\).[4]
2. The function can also be expressed as \(f(x)=a\sin\left(b(x+d)\right)+c\), using the values of \(a\), \(b\) and \(c\) found in part (a). Find the smallest positive value of \(d\).[2]
3. Solve the equation \(2f(x)=7\) for \(-4\le x\le10\).[2]