ANSWER
[tex]y=\sin \mleft(\frac{1}{4}x\mright)-3[/tex]
EXPLANATION
The sine function has the form,
[tex]y=A\sin (Bx)+C[/tex]
Where A is the amplitude, C is the vertical shift, and B is related with the period,
[tex]T=\frac{2\pi}{B}[/tex]
We can obtain all this information from the graph,
The period is 8π, so B is,
[tex]B=\frac{2\pi}{T}=\frac{2\pi}{8\pi}=\frac{1}{4}[/tex]
The amplitude is 1 and the function is shifted 3 units down, so C = -3.
Hence, the equation is,
[tex]y=\sin \mleft(\frac{1}{4}x\mright)-3[/tex]
