Note that in any sine function :
[tex]y=A\sin (B(x+C))+D[/tex]Amplitude = A
Verical Shift or midline = D
Period = (2π)/B
Horizontal or Phase Shift = C
From the given,
since we dont have any horizontal shift, C = 0.
Amplitude = 5, so A = 5
Midline = 4, so D = 4
and
Period = 3/2, so equating it to (2 π)/B
[tex]\frac{3}{2}=\frac{2\pi}{B}[/tex][tex]B=\frac{4\pi}{3}[/tex]Now, substituting the values obtained, the sine function will be :
[tex]y=5\sin (\frac{4\pi}{3}x)+4[/tex]