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

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Author: Washington

Publisher: PEARSON

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Chapter 10.3, Problem 23E

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The value of amplitude, period and displacement for the function y=sin(π2x−π), sketch the graph of the function and check using a calculator.

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Chapter 10.3, Problem 22E

Chapter 10.3, Problem 24E

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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 = sin ( π 2 x − π ) , 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=sin(π2x−π), sketch the graph of the function and check using a calculator.

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Chapter 10 Solutions