The graph shown is the curve given by $y = a\sin(bx) + c$ for $0 \leq x \leq 2\pi$, with $a$, $b$ and $c$ all positive constants.
(a)[3]
State the values of $a$, $b$ and $c$.
(b(i))[1]
Using these values of $a$, $b$ and $c$, find the number of solutions in the interval $0 \leq x \leq 2\pi$ for the equation $a\sin(bx) + c = 7 - x$.
(b(ii))[1]
Using these values of $a$, $b$ and $c$, find the number of solutions in the interval $0 \leq x \leq 2\pi$ for the equation $a\sin(bx) + c = 2\pi(x - 1)$.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The value of $a$ is $4$.” …