Answer:[tex]y=4sin(\frac{\pi }{6} x+\frac{\pi }{2} )[/tex]
Step-by-step explanation:
We start from the general form of the sine function which is:
[tex]y=a sin(bx+c)[/tex]
where
Amplitude= IaI=[tex]\frac{8}{2}[/tex]=4( which is the maximum value we have above the 0 axis)
Period=[tex]\frac{2\pi }{b}[/tex]
Period=12 (space between high tides)
Isolating b:
[tex]b=\frac{1}{6} \pi[/tex]
Horizontal shift = c (Normally the function starts at 0 but in the excercise we have at midnight hight tide this meaning the function is at its maximum value so we need to move it a quarter of the period so it will have maximum value at t=0)
[tex]c=\frac{\pi }{2}[/tex]
then
[tex]y=4sin(\frac{\pi }{6} x+\frac{\pi }{2} )[/tex]
