Answer:
A [tex]y=8\sin \dfrac{1}{2}x[/tex]
Step-by-step explanation:
From the graph you can see that the period of the function is
[tex]720^{\circ}=4\pi[/tex]
Now the period of the function [tex]y=8\sin kx[/tex] is
[tex]T=\dfrac{2\pi}{k}[/tex]
Thus,
[tex]4\pi=\dfrac{2\pi}{k}\Rightarrow 4\pi k=2\pi\\ \\k=\dfrac{2\pi}{4\pi}=\dfrac{1}{2}[/tex]
and the expression for the function is
[tex]y=8\sin \dfrac{1}{2}x[/tex]
