Trigonometry

Let \[\mathrm{f}(x)=a\sin x+b\cos x,\] where \(a,b>0\).
Over \(0^\circ\le x<360^\circ\), the maximum value of \(\mathrm{f}(x)\) is \(10\), occurring at \(x=30^\circ\).
Find \(a\) and \(b\) exactly. Justify how the location of the maximum determines the phase angle.