Explanation Result used: The functions y = a sin b x or y = a cos b x each has an amplitude of | a | and a period of 2 π b . Calculation: Given that, the tides have water level about 4m between the low and high tides on a Florida beach. Thus, the amplitude will be half of the water level between the low and high tides. That is, a = 4 m 2 = 2 m The period is given as, 12.5h. By the above mentioned result, 2 π b = 12.5 . Simplify further as, 2 π b = 12.5 b = 2 π 12.5 b = 4 π 25 That is, the values of a and b are 2 and 4 π 25 , respectively. Thus, the maximum and minimum values are 2 and –2, respectively. Substitute a = 2 and b = 4 π 25 in the cosine function y = a cos b x to obtain as, y = 2 cos ( 4 π 25 x ) . Therefore, the cosine function that describes the tides if the high tide is at midnight is y = 2 cos ( 4 π 25 x ) _ . It is known that an important distance in sketching a sine or cosine curve is the values of the function for each one-fourth period. Thus, one-fourth of the period will be, 1 4 ( 12.5 ) = 3.125 . Substitute x = 0 in the equation y = 2 cos ( 4 π 25 x ) . y = 2 cos ( 4 π 25 x ) = 2 cos ( 4 π 25 × 0 ) = 2 cos ( 0 ) = 2 ( 1 ) = 2 That is, when x = 0 , the value of y is the maximum value 2

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 10.2, Problem 42E

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The cosine function that describes the tides if the high tide is at midnight and sketch the graph.

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Chapter 10.2, Problem 41E

Chapter 10.2, Problem 43E

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Ch. 10.1 - For the graph of y = −6 sin x, set up a table of...Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - In Exercises 3–6, complete the following table for...Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - In Exercises 7–22, give the amplitude and sketch...Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E

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