1.3: Sine curve: constants and sketch

The curve $y = a + b\sin cx$ has an amplitude of $4$ and a period of $\tfrac{\pi}{3}$. Given that the curve passes through the point $\left(\tfrac{\pi}{12}, 2\right)$, find the value of each of the constants $a$, $b$ and $c$.

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