) Use sinusoidal functions to find the depth d(t) of the water, in meters, as a function of time t in hours.

Due to the high and low tides, the depth d of water in a certain costal area may be expressed by a sinusoidal function. The highest tide occurs at 8 am and the lowest tide occurs 6 hours later. The maximum level of water is 2.8 meters and the lowest level of water is 0.4 meters.
a) Use sinusoidal functions to find the depth d(t) of the water, in meters, as a function of time t in hours. (Assume that 8 am corresponds to t = 0).
b) Find the depth of water at noon.
c) Use the graph of d(t) and analytical calculations to calculate the interval of time during which the depth d is below 1.5 m from 12 pm to 6 pm.

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