Tides and water depth trig problems

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  1. Tides are a periodic rise and fall of water in the ocean. At a seaport, the water has a minimum depth of 4m at 3:00 am. After this minimum depth, the first maximum depth of 20m occurs at 10:30 am.
    1. Graph how the depth of the tide flow varies with respect to the time in a day.
    2. Determine a sinusoidal function for the water depth at any time t.
    3. What is the water depth at 6:45pm?
    4. A cruise ship needs at least 9m of water to dock safely. Estimate the number of hours in the 24 hour interval during which the cruise ship can dock safely.