The function \(f\) is defined, for \(0^\circ\leq x\leq360^\circ\), by \(f(x)=a+b\sin cx\), where \(a\), \(b\) and \(c\) are constants with \(b\gt 0\) and \(c\gt 0\). The graph of \(y=f(x)\) meets the \(y\)-axis at the point \((0,-1)\), has a period of \(120^\circ\) and an amplitude of \(5\).

(i) Sketch the graph of \(y=f(x)\).

(ii) Write down the value of each of the constants \(a\), \(b\) and \(c\).