(i) The curve

\(y=a+b\sin cx\)

has an amplitude of \(4\) and a period of \(\dfrac{\pi}{3}\). Given that the curve passes through the point \(\left(\dfrac{\pi}{12},2\right)\), find the value of each of the constants \(a\), \(b\) and \(c\).

(ii) Using your values of \(a\), \(b\) and \(c\), sketch the graph of \(y=a+b\sin cx\) for \(0\leq x\leq\pi\) radians.