Question

Tidal forces are greatest when the Eaetg, the sun and the moon are in line. When this occurs at the Annapolis Tidal Generating Station, the waterhas a maximum depth of 9.6 m at 4:30 pm and a minimum depthof 0.4 m 6.2 hourslater.

the equation is:
y= 4.6cos (2pi/12.4) (t-4.5) + 5

I don't know how the phase shift was determined.

What is the depth of the water at 9:30 am and 6:45 pm??

Answer 1

In your equation, t is the number of hours past noon.

At 9:30 AM, use your equation with t = -2.5 (hours)

At 6:45 PM, use your equation at 2.25 h.

Cosine function fits to tidal variations, such as this, are not good for much more than 12 hours. The amplitude is constantly changing.