Explanation Result 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: The given function is y = π cos ( 1 π x + 1 3 ) . Compare the equations y = a cos ( b x + c ) and y = π cos ( 1 π x + 1 3 ) . Thus, a = π , b = 1 π and c = 1 3 . By the above mentioned result, the amplitude of y = π cos ( 1 π x + 1 3 ) will be, | a | = | π | ( ∵ a = π ) = π That is, the maximum value will be π and the minimum value will be − π . The period is obtained as follows: 2 π b = 2 π ( 1 π ) ( ∵ b = 1 π ) = 2 π 2 The displacement is obtained as follows: − c b = − ( 1 3 ) ( 1 π ) ( ∵ b = 1 π and c = 1 3 ) = − π 3 Therefore, the amplitude, period and displacement for the function y = π cos ( 1 π x + 1 3 ) is π , 2 π 2 and − π 3 _ , 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 ( 2 π 2 ) = π 2 2 . That is, the curve starts at − π 3 and starts repeating 2 π 2 units to the right of − π 3 . Since the period is 2 π 2 , the one complete cycle of the curve ends at 2 π 2 − π 3 . That is, one complete cycle is from x = − π 3 to x = 2 π 2 − π 3

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ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Fundamentals of Trigonometric Identities

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Chapter 10.3, Problem 26E

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The value of amplitude, period and displacement for the function y=πcos(1πx+13), sketch the graph of the function and check using a calculator.

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Chapter 10.3, Problem 25E

Chapter 10.3, Problem 27E

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Chapter 10 Solutions

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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

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 value of amplitude, period and displacement for the function y = π cos ( 1 π x + 1 3 ) , sketch the graph of the function and check using a calculator.

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The value of amplitude, period and displacement for the function y=πcos(1πx+13), sketch the graph of the function and check using a calculator.

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Chapter 10 Solutions