Explanation Formula used: The functions y = a sin ( b x + c ) or y = a cos ( b x + c ) each has an amplitude of | a | , period of 2 π b and displacement is − c b . Calculation: From the given curve, it is observed that the maximum value is 5 and the minimum value is –5. Thus, the amplitude of the given curve will be, a = 5 . The one complete cycle occurs between x = − 1 and x = 15 . Thus, the period of the given curve will be, 15 − ( − 1 ) = 16 . The given curve should be of the specific form y = a cos ( b x + c ) . Notice that, the cosine function has its maximum at 0. One fourth of the period of the given curve will be 1 4 ( 16 ) = 4 . Thus, the maximum of the given curve occurs at − 1 + 4 = 3 . The given graph has its maximum when x = 3 . That is, the displacement of the cosine function for the given curve is 3. By the above mentioned formula, a = 5 , 2 π b = 16 and − c b = 3

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

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Author: Allyn Washington, Richard Evans

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Chapter 10.3, Problem 42E

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The specific form of the equation y=acos(bx+c) by evaluating the values of a, b and c through the inspection of the given curve.

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Chapter 10.3, Problem 41E

Chapter 10.3, Problem 43E

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Chapter 10 Solutions

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

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

Ch. 10.1 - Prob. 10E Ch. 10.1 - Prob. 11E Ch. 10.1 - Prob. 12E Ch. 10.1 - In Exercises 7–22, give the amplitude and sketch...Ch. 10.1 - In Exercises 7–22, give the amplitude and sketch...Ch. 10.1 - Prob. 15E Ch. 10.1 - Prob. 16E Ch. 10.1 - Prob. 17E Ch. 10.1 - Prob. 18E Ch. 10.1 - Prob. 19E Ch. 10.1 - Prob. 20E Ch. 10.1 - Prob. 21E Ch. 10.1 - Prob. 22E Ch. 10.1 - Prob. 23E Ch. 10.1 - Prob. 24E Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - Prob. 28E Ch. 10.1 - Prob. 29E Ch. 10.1 - Prob. 30E Ch. 10.1 - Prob. 31E Ch. 10.1 - In Exercises 27–32, solve the given problems. 32....Ch. 10.1 - Prob. 33E Ch. 10.1 - Prob. 34E Ch. 10.1 - Prob. 35E Ch. 10.1 - Prob. 36E Ch. 10.1 - Prob. 37E Ch. 10.1 - Prob. 38E Ch. 10.1 - Prob. 39E Ch. 10.1 - Prob. 40E Ch. 10.2 - Prob. 1PE Ch. 10.2 - Prob. 2PE Ch. 10.2 - Prob. 3PE Ch. 10.2 - Prob. 1E Ch. 10.2 - Prob. 2E Ch. 10.2 - Prob. 3E Ch. 10.2 - In Exercises 3–22, find the amplitude and period...Ch. 10.2 - Prob. 5E Ch. 10.2 - In Exercises 3–22, find the amplitude and period...Ch. 10.2 - 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Prob. 43E Ch. 10.2 - Prob. 44E Ch. 10.2 - Prob. 45E Ch. 10.2 - Prob. 46E Ch. 10.3 - Prob. 1PE Ch. 10.3 - Prob. 2PE Ch. 10.3 - Prob. 1E Ch. 10.3 - Prob. 2E Ch. 10.3 - In Exercises 3–26, determine the amplitude,...Ch. 10.3 - In Exercises 3–26, determine the amplitude,...Ch. 10.3 - In Exercises 3–26, determine the amplitude,...Ch. 10.3 - In Exercises 3–26, determine the amplitude,...Ch. 10.3 - Prob. 7E Ch. 10.3 - Prob. 8E Ch. 10.3 - Prob. 9E Ch. 10.3 - Prob. 10E Ch. 10.3 - Prob. 11E Ch. 10.3 - Prob. 12E Ch. 10.3 - Prob. 13E Ch. 10.3 - Prob. 14E Ch. 10.3 - Prob. 15E Ch. 10.3 - Prob. 16E Ch. 10.3 - Prob. 17E Ch. 10.3 - In Exercises 3–26, determine the amplitude,...Ch. 10.3 - Prob. 19E Ch. 10.3 - In Exercises 3–26, determine the amplitude,...Ch. 10.3 - Prob. 21E Ch. 10.3 - Prob. 22E Ch. 10.3 - Prob. 23E Ch. 10.3 - Prob. 24E Ch. 10.3 - Prob. 25E Ch. 10.3 - Prob. 26E Ch. 10.3 - Prob. 27E Ch. 10.3 - Prob. 28E Ch. 10.3 - Prob. 29E Ch. 10.3 - Prob. 30E Ch. 10.3 - Prob. 31E Ch. 10.3 - Prob. 32E Ch. 10.3 - 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The specific form of the equation y = a cos ( b x + c ) by evaluating the values of a , b and c through the inspection of the given curve.

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The specific form of the equation y=acos(bx+c) by evaluating the values of a, b and c through the inspection of the given curve.

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Chapter 10 Solutions