Please help me with the questions below. In a tidal river, the time between high tide and low tide is 6.2 hours. At high tide the depth of the water is 17.2 feet, while at low tide the depth is 5.6 feet. Assume the water depth is a sinusoidal function of time (i.e., could model with either a cosine or sine function). Sketch a graph the depth of the water over time if there is a high tide at 12:00 noon. Assume that noon is represented by t = 0. Label your graph, including high tide and low tide. You must space your tick marks on the horizontal axis by one-quarter of the cycle. Graph two full periods of the function and label each point that is a maximum, minimum, or midline point. Write an equation for the function. You must show how to determine essential features such as the amplitude, period, midline, and any potential other shifts. A boat requires a depth of 8 feet to sail and is docked at 12:00 noon. What is the latest time in the afternoon, the boat can set sail? Your answer should be accurate to the nearest minute. You should note that there is something intentionally vague about this problem and some missing information. You should consider your graph and state any assumptions you are making that clarify your solution. You must provide an analytical solution. You can appeal to a graph for help, but you must have at least an analytical portion of your solution that finds one solution/intersection point.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.5: Trigonometric Graphs

Problem 6E

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Please help me with the questions below.

In a tidal river, the time between high tide and low tide is 6.2 hours. At high tide the depth of the water is 17.2 feet, while at low tide the depth is 5.6 feet. Assume the water depth is a sinusoidal function of time (i.e., could model with either a cosine or sine function).

Sketch a graph the depth of the water over time if there is a high tide at 12:00 noon. Assume that noon is represented by t = 0. Label your graph, including high tide and low tide. You must space your tick marks on the horizontal axis by one-quarter of the cycle. Graph two full periods of the function and label each point that is a maximum, minimum, or midline point.
Write an equation for the function. You must show how to determine essential features such as the amplitude, period, midline, and any potential other shifts.
A boat requires a depth of 8 feet to sail and is docked at 12:00 noon. What is the latest time in the afternoon, the boat can set sail? Your answer should be accurate to the nearest minute. You should note that there is something intentionally vague about this problem and some missing information. You should consider your graph and state any assumptions you are making that clarify your solution. You must provide an analytical solution. You can appeal to a graph for help, but you must have at least an analytical portion of your solution that finds one solution/intersection point.

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