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: The given function is y = 0.4 sin 2 π x 9 . Compare the equations y = 0.4 sin 2 π x 9 and y = a sin b x . Thus, a = 0.4 and b = 2 π 9 . By the above mentioned result, the amplitude of y = 0.4 sin 2 π x 9 is | 0.4 | = 0.4 . That is, the maximum value will be 0.4 and the minimum value will be –0.4. The period is obtained as follows: 2 π b = 2 π ( 2 π 9 ) ( ∵ b = 2 π 9 ) = 9 Thus, the amplitude and period of the function y = 0.4 sin 2 π x 9 is 0 .4 and 9 _ , respectively. 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 ( 9 ) = 9 4 . Substitute x = 0 in the equation y = 0.4 sin 2 π x 9 . y = 0.4 sin 2 π x 9 = 0.4 sin ( 2 π 9 × 0 ) = 0.4 sin ( 0 ) = 0

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

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ISBN: 9780137554843

Author: Allyn Washington, Richard Evans

Publisher: PEARSON+

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Chapter 10.2, Problem 19E

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The amplitude and period of the function y=0.4sin2πx9 and sketch the graph.

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Chapter 10.2, Problem 18E

Chapter 10.2, Problem 20E

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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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The amplitude and period of the function y = 0.4 sin 2 π x 9 and sketch the graph.

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The amplitude and period of the function y=0.4sin2πx9 and sketch the graph.

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Chapter 10 Solutions