To determine The value of amplitude, period and displacement for the function y = sin ( x − π 6 ) , sketch the graph of the function and check using a calculator. 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 ( x − π 6 ) . Compare the equations y = a sin ( b x + c ) and y = sin ( x − π 6 ) . Thus, a = 1 , b = 1 and c = − π 6 . By the above mentioned result, the amplitude of y = sin ( x − π 6 ) 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 1 ( ∵ b = 1 ) = 2 π The displacement is obtained as follows: − c b = − ( − π 6 ) 1 ( ∵ b = 1 and c = − π 6 ) = π 6 Therefore, the amplitude, period and displacement for the function y = sin ( x − π 6 ) is 1 , 2 π and π 6 _ , respectively. It is known that an important quantity 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 ) = π 2 . That is, the curve starts at π 6 and starts repeating 2 π units to the right of π 6 . Since the period is 2 π , the one complete cycle of the curve ends at π 6 + 2 π = 13 π 6

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

11th Edition

ISBN: 9780137554843

Author: Allyn Washington, Richard Evans

Publisher: PEARSON+

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Chapter 10.3, Problem 3E

To determine

The value of amplitude, period and displacement for the function y=sin(x−π6), sketch the graph of the function and check using a calculator.

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Chapter 10.3, Problem 2E

Chapter 10.3, Problem 4E

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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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