Period, maximum value and single-sine form of a combination of sin 4x and cos 4x

The function \(\mathrm{g}\) is defined by \(\mathrm{g}(x)=8\sin4x-15\cos4x\) for \(x\in\mathbb{R}\).

1. Determine the exact period of \(\mathrm{g}\).[2]
2. Find the greatest value taken by \(\mathrm{g}(x)\).[1]
3. It is given that \(\mathrm{g}(x)=R\sin(kx-\alpha)\), where \(R>0\), \(k>0\) and \(0<\alpha<\frac{\pi}{2}\).
   1. Find the value of \(R\).
   2. Write down the value of \(k\).
   3. Find the value of \(\alpha\).[4]