Modeling Periodic Phenomena with Trigonometric Functions Throughout any given month, the maximum and minimum ocean tides follow a periodic pattern. Last year, at a certain location on the California coast, researchers recorded the height of low tide, with respect to sea level, each day during the month of July. The lowest low tide was first measured on July 11, at -1.4 feet. The highest low tide was first measured on July 4, at 1.8 feet. The average low tide for the month of July was measured to be 0.2 feet. Part A Why do the ocean tides follow a periodic pattern? Part C Which curve would you choose to model this function, sine or cosine? Give your reasons. Part D Find the amplitude of the function. Explain its meaning in the context. Part E Find the period of the function. Explain its meaning in the context. Part F Find the vertical shift of the function. Explain its meaning in the context Part G Find the phase shift of the function. Explain its meaning in context. Part H Write the function for the curve from all of the key features you just found. Part I Graph the function on the grid from part C, where you plotted the two given points. Part J What are the days of the month when the low tide is projected to be the average height? What do you suppose a decimal value for a day in the month means? Part K The actual low tide height recorded on a given day could vary from the function created as a model. Give some reasons for why you think this happens.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Modeling Periodic Phenomena with Trigonometric Functions

Throughout any given month, the maximum and minimum ocean tides follow a periodic pattern. Last year, at a certain location on the California coast, researchers recorded the height of low tide, with respect to sea level, each day during the month of July. The lowest low tide was first measured on July 11, at -1.4 feet. The highest low tide was first measured on July 4, at 1.8 feet. The average low tide for the month of July was measured to be 0.2 feet.

Part A

Why do the ocean tides follow a periodic pattern?

Part C

Which curve would you choose to model this function, sine or cosine? Give your reasons.

Part D

Find the amplitude of the function. Explain its meaning in the context.

Part E

Find the period of the function. Explain its meaning in the context.

Part F

Find the vertical shift of the function. Explain its meaning in the context

Part G

Find the phase shift of the function. Explain its meaning in context.

Part H

Write the function for the curve from all of the key features you just found.

Part I

Graph the function on the grid from part C, where you plotted the two given points.

Part J

What are the days of the month when the low tide is projected to be the average height? What do you suppose a decimal value for a day in the month means?