2. Please read the following paragraph carefully and build a cosine model based on the data given. Suppose that you are on the beach on December 25 and notice that the high tide occurs at 3:00 PM with a depth of 1.5 meters. You then return at 8:00 PM in the evening and notice it is low tide at 0.3 meters. Since tides vary sinusoidally over time, find a cosine function that represents the depth of the tide as a function of time x measured in hours after 12:00 AM on December 25th.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.7: Applied Problems
Problem 68E
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2. Please read the following paragraph carefully and build a cosine model based on the data given.
Suppose that you are on the beach on December 25 and notice that the high tide occurs at 3:00 PM
with a depth of 1.5 meters. You then return at 8:00 PM in the evening and notice it is low tide at 0.3
meters. Since tides vary sinusoidally over time, find a cosine function that represents the depth of
the tide as a function of time x measured in hours after 12:00 AM on December 25th.
a) Determine the following characteristics of the cosine function from the given information:
Maximum value
Minimum value
Period T =
Horizontal shift p
=
hours
m
m
m
hours
b) Now compute the relevant parameters for the equation:
Amplitude A =
Average value D =
Frequency B
c) Write a cosine function that models the height of the tide. Use exact values.
f(x) =_
m
Transcribed Image Text:2. Please read the following paragraph carefully and build a cosine model based on the data given. Suppose that you are on the beach on December 25 and notice that the high tide occurs at 3:00 PM with a depth of 1.5 meters. You then return at 8:00 PM in the evening and notice it is low tide at 0.3 meters. Since tides vary sinusoidally over time, find a cosine function that represents the depth of the tide as a function of time x measured in hours after 12:00 AM on December 25th. a) Determine the following characteristics of the cosine function from the given information: Maximum value Minimum value Period T = Horizontal shift p = hours m m m hours b) Now compute the relevant parameters for the equation: Amplitude A = Average value D = Frequency B c) Write a cosine function that models the height of the tide. Use exact values. f(x) =_ m
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