We need to find the period of the sinusoidal function in this case we have the next form
[tex]y=A\sin \frac{2\pi}{T}(x+a)+b[/tex]
First, we need to find the amplitude in this case
[tex]A=\frac{5+1}{2}=\frac{6}{2}=3[/tex]
The amplitude is 3
Then we need to find the period
[tex]T=\frac{2\pi}{3}[/tex]
and the the displacement b is 2
Then for a we have
[tex]a=\frac{5}{12}\pi[/tex]
Therefore we have
[tex]y=3\sin 3(x-\frac{5\pi}{12})+2[/tex]
ANSWER
[tex]y=3\sin 3(x-\frac{5\pi}{12})+2[/tex]
