Problem

The diagram shows the curve with equation $y=a\sin(bx)+c$ for $0\leq x\leq 2\pi$, where $a$, $b$ and $c$ are positive constants.

(a) State the values of $a$, $b$ and $c$.

(b) For these values of $a$, $b$ and $c$, determine the number of solutions in the interval $0\leq x\leq 2\pi$ for each of the following equations:

(i) $a\sin(bx)+c=7-x$

(ii) $a\sin(bx)+c=2\pi(x-1)$.