To determine The value of amplitude, period and displacement for the function y = 2 cos ( x − π 8 ) , 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 = 2 cos ( x − π 8 ) . Compare the equations y = a cos ( b x + c ) and y = 2 cos ( x − π 8 ) . Thus, a = 2 , b = 1 and c = − π 8 . By the above mentioned result, the amplitude of y = 2 cos ( x − π 8 ) will be, | a | = | 2 | ( ∵ a = 2 ) = 2 That is, the maximum value will be 2 and the minimum value will be –2. 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 8 ) 1 ( ∵ b = 1 and c = − π 8 ) = π 8 Therefore, the amplitude, period and displacement for the function y = 2 cos ( x − π 8 ) is 2 , 2 π and π 8 _ , 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 8 and starts repeating 2 π units to the right of π 8 . Since the period is 2 π , the one complete cycle of the curve ends at π 8 + 2 π = 17 π 8

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 10.3, Problem 6E

To determine

The value of amplitude, period and displacement for the function y=2cos(x−π8), sketch the graph of the function and check using a calculator.

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Chapter 10.3, Problem 5E

Chapter 10.3, Problem 7E

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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

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