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 = − 1 2 cos 2 3 x . Compare the equations y = − 1 2 cos 2 3 x and y = a cos b x . Thus, a = − 1 2 and b = 2 3 . By the above mentioned result, the amplitude of y = − 1 2 cos 2 3 x is | − 1 2 | = 1 2 . That is, the maximum value will be 1 2 and the minimum value will be − 1 2 . The period is obtained as follows: 2 π b = 2 π ( 2 3 ) ( ∵ b = 2 3 ) = 3 π Thus, the amplitude and period of the function y = − 1 2 cos 2 3 x is 1 2 and 3 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 ( 3 π ) = 3 π 4 . Substitute x = 0 in the equation y = − 1 2 cos 2 3 x . y = − 1 2 cos 2 3 x = − 1 2 cos ( 2 3 × 0 ) = − 1 2 cos ( 0 ) = − 1 2 ( 1 ) = − 1 2 That is, when x = 0 the value of y is − 1 2 , which is a minimum point

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780134434636

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 10.2, Problem 17E

To determine

The amplitude and period of the function y=−12cos23x and sketch the graph.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 10.2, Problem 16E

Chapter 10.2, Problem 18E

Students have asked these similar questions

The Martinezes are planning to refinance their home. The outstanding balance on their original loan is $150,000. Their finance company has offered them two options. (Assume there are no additional finance charges. Round your answers to the nearest cent.) Option A: A fixed-rate mortgage at an interest rate of 4.5%/year compounded monthly, payable over a 30-year period in 360 equal monthly installments.Option B: A fixed-rate mortgage at an interest rate of 4.25%/year compounded monthly, payable over a 12-year period in 144 equal monthly installments. (a) Find the monthly payment required to amortize each of these loans over the life of the loan. option A $ option B $ (b) How much interest would the Martinezes save if they chose the 12-year mortgage instead of the 30-year mortgage?

Given: Circle J 2 What is the value of y? A. 38 C. 68 B. 50 D. 92

Chapter 10 Solutions

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

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 - Prob. 7E Ch. 10.2 - In Exercises 3–22, find the amplitude and period...Ch. 10.2 - In Exercises 3–22, find the amplitude and period...Ch. 10.2 - Prob. 10E Ch. 10.2 - Prob. 11E Ch. 10.2 - Prob. 12E Ch. 10.2 - Prob. 13E Ch. 10.2 - In Exercises 3–22, find the amplitude and period...Ch. 10.2 - Prob. 15E Ch. 10.2 - Prob. 16E Ch. 10.2 - Prob. 17E Ch. 10.2 - Prob. 18E Ch. 10.2 - Prob. 19E Ch. 10.2 - Prob. 20E Ch. 10.2 - Prob. 21E Ch. 10.2 - Prob. 22E Ch. 10.2 - Prob. 23E Ch. 10.2 - In Exercises 23–26, the period is given for a...Ch. 10.2 - Prob. 25E Ch. 10.2 - In Exercises 23–26, the period is given for a...Ch. 10.2 - Prob. 27E Ch. 10.2 - Prob. 28E Ch. 10.2 - Prob. 29E Ch. 10.2 - Prob. 30E Ch. 10.2 - Prob. 31E Ch. 10.2 - Prob. 32E Ch. 10.2 - Prob. 33E Ch. 10.2 - Prob. 34E Ch. 10.2 - Prob. 35E Ch. 10.2 - In Exercises 31–36, solve the given...Ch. 10.2 - Prob. 37E Ch. 10.2 - Prob. 38E Ch. 10.2 - In Exercises 39–42, graph the indicated...Ch. 10.2 - Prob. 40E Ch. 10.2 - Prob. 41E Ch. 10.2 - Prob. 42E Ch. 10.2 - 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 - Prob. 33E Ch. 10.3 - Prob. 34E Ch. 10.3 - Prob. 35E Ch. 10.3 - Prob. 36E Ch. 10.3 - Prob. 37E Ch. 10.3 - Prob. 38E Ch. 10.3 - Prob. 39E Ch. 10.3 - Prob. 40E Ch. 10.3 - Prob. 41E Ch. 10.3 - Prob. 42E Ch. 10.3 - In Exercises 41–44, give the specific form of the...Ch. 10.3 - Prob. 44E Ch. 10.4 - In Exercises 1 and 2, view the graphs on a...Ch. 10.4 - Prob. 2E Ch. 10.4 - Prob. 3E Ch. 10.4 - Prob. 4E Ch. 10.4 - Prob. 5E Ch. 10.4 - Prob. 6E Ch. 10.4 - Prob. 7E Ch. 10.4 - Prob. 8E Ch. 10.4 - Prob. 9E Ch. 10.4 - Prob. 10E Ch. 10.4 - Prob. 11E Ch. 10.4 - Prob. 12E Ch. 10.4 - Prob. 13E Ch. 10.4 - Prob. 14E Ch. 10.4 - Prob. 15E Ch. 10.4 - In Exercises 15–24, view at least two cycles of...Ch. 10.4 - Prob. 17E Ch. 10.4 - Prob. 18E Ch. 10.4 - Prob. 19E Ch. 10.4 - Prob. 20E Ch. 10.4 - Prob. 21E Ch. 10.4 - Prob. 22E Ch. 10.4 - Prob. 23E Ch. 10.4 - Prob. 24E Ch. 10.4 - Prob. 25E Ch. 10.4 - Prob. 26E Ch. 10.4 - Prob. 27E Ch. 10.4 - Prob. 28E Ch. 10.4 - Prob. 29E Ch. 10.4 - Prob. 30E Ch. 10.4 - Prob. 31E Ch. 10.4 - Prob. 32E Ch. 10.5 - Prob. 1PE Ch. 10.5 - Prob. 2PE Ch. 10.5 - Prob. 1E Ch. 10.5 - Prob. 2E Ch. 10.5 - Prob. 3E Ch. 10.5 - Prob. 4E Ch. 10.5 - Prob. 5E Ch. 10.5 - Prob. 6E Ch. 10.5 - Prob. 7E Ch. 10.5 - Prob. 8E Ch. 10.5 - Prob. 9E Ch. 10.5 - Prob. 10E Ch. 10.5 - Prob. 11E Ch. 10.5 - Prob. 12E Ch. 10.5 - Prob. 13E Ch. 10.5 - Prob. 14E Ch. 10.5 - Prob. 15E Ch. 10.5 - Prob. 16E Ch. 10.5 - Prob. 17E Ch. 10.5 - Prob. 18E Ch. 10.5 - Prob. 19E Ch. 10.5 - Prob. 20E Ch. 10.5 - Prob. 21E Ch. 10.5 - Prob. 22E Ch. 10.5 - Prob. 23E Ch. 10.5 - Prob. 24E Ch. 10.5 - Prob. 25E Ch. 10.5 - Prob. 26E Ch. 10.6 - Prob. 1E Ch. 10.6 - Prob. 2E Ch. 10.6 - Prob. 3E Ch. 10.6 - Prob. 4E Ch. 10.6 - Prob. 5E Ch. 10.6 - Prob. 6E Ch. 10.6 - Prob. 7E Ch. 10.6 - Prob. 8E Ch. 10.6 - Prob. 9E Ch. 10.6 - Prob. 10E Ch. 10.6 - Prob. 11E Ch. 10.6 - Prob. 12E Ch. 10.6 - Prob. 13E Ch. 10.6 - Prob. 14E Ch. 10.6 - Prob. 15E Ch. 10.6 - Prob. 16E Ch. 10.6 - Prob. 17E Ch. 10.6 - Prob. 18E Ch. 10.6 - Prob. 19E Ch. 10.6 - Prob. 20E Ch. 10.6 - Prob. 21E Ch. 10.6 - Prob. 22E Ch. 10.6 - Prob. 23E Ch. 10.6 - Prob. 24E Ch. 10.6 - Prob. 25E Ch. 10.6 - Prob. 26E Ch. 10.6 - Prob. 27E Ch. 10.6 - Prob. 28E Ch. 10.6 - Prob. 29E Ch. 10.6 - Prob. 30E Ch. 10.6 - Prob. 31E Ch. 10.6 - Prob. 32E Ch. 10.6 - Prob. 33E Ch. 10.6 - Prob. 34E Ch. 10.6 - Prob. 35E Ch. 10.6 - Prob. 36E Ch. 10.6 - Prob. 37E Ch. 10.6 - Prob. 38E Ch. 10.6 - Prob. 39E Ch. 10.6 - Prob. 40E Ch. 10.6 - Prob. 41E Ch. 10.6 - Prob. 42E Ch. 10.6 - Prob. 43E Ch. 10.6 - Prob. 44E Ch. 10.6 - Prob. 45E Ch. 10.6 - Prob. 46E Ch. 10.6 - Prob. 47E Ch. 10.6 - Prob. 48E Ch. 10.6 - Prob. 49E Ch. 10.6 - Prob. 50E Ch. 10 - Prob. 1RE Ch. 10 - Prob. 2RE Ch. 10 - Prob. 3RE Ch. 10 - Prob. 4RE Ch. 10 - Prob. 5RE Ch. 10 - Prob. 6RE Ch. 10 - Prob. 7RE Ch. 10 - Prob. 8RE Ch. 10 - Prob. 9RE Ch. 10 - Prob. 10RE Ch. 10 - Prob. 11RE Ch. 10 - Prob. 12RE Ch. 10 - Prob. 13RE Ch. 10 - Prob. 14RE Ch. 10 - Prob. 15RE Ch. 10 - Prob. 16RE Ch. 10 - Prob. 17RE Ch. 10 - Prob. 18RE Ch. 10 - Prob. 19RE Ch. 10 - In Exercises 7–34, sketch the curves of the given...Ch. 10 - Prob. 21RE Ch. 10 - Prob. 22RE Ch. 10 - Prob. 23RE Ch. 10 - Prob. 24RE Ch. 10 - Prob. 25RE Ch. 10 - Prob. 26RE Ch. 10 - Prob. 27RE Ch. 10 - Prob. 28RE Ch. 10 - Prob. 29RE Ch. 10 - Prob. 30RE Ch. 10 - Prob. 31RE Ch. 10 - Prob. 32RE Ch. 10 - Prob. 33RE Ch. 10 - Prob. 34RE Ch. 10 - Prob. 35RE Ch. 10 - Prob. 36RE Ch. 10 - Prob. 37RE Ch. 10 - Prob. 38RE Ch. 10 - Prob. 39RE Ch. 10 - In Exercises 39–46, display the curves of the...Ch. 10 - Prob. 41RE Ch. 10 - Prob. 42RE Ch. 10 - Prob. 43RE Ch. 10 - Prob. 44RE Ch. 10 - Prob. 45RE Ch. 10 - Prob. 46RE Ch. 10 - Prob. 47RE Ch. 10 - Prob. 48RE Ch. 10 - Prob. 49RE Ch. 10 - Prob. 50RE Ch. 10 - Prob. 51RE Ch. 10 - Prob. 52RE Ch. 10 - Prob. 53RE Ch. 10 - Prob. 54RE Ch. 10 - Prob. 55RE Ch. 10 - Prob. 56RE Ch. 10 - Prob. 57RE Ch. 10 - Prob. 58RE Ch. 10 - Prob. 59RE Ch. 10 - Prob. 60RE Ch. 10 - Prob. 61RE Ch. 10 - Prob. 62RE Ch. 10 - Prob. 63RE Ch. 10 - Prob. 64RE Ch. 10 - Prob. 65RE Ch. 10 - Prob. 66RE Ch. 10 - Prob. 67RE Ch. 10 - Prob. 68RE Ch. 10 - Prob. 69RE Ch. 10 - Prob. 70RE Ch. 10 - Prob. 71RE Ch. 10 - Prob. 72RE Ch. 10 - Prob. 73RE Ch. 10 - Prob. 74RE Ch. 10 - Prob. 75RE Ch. 10 - Prob. 76RE Ch. 10 - Prob. 77RE Ch. 10 - Prob. 78RE Ch. 10 - Prob. 79RE Ch. 10 - Prob. 80RE Ch. 10 - Prob. 81RE Ch. 10 - Prob. 82RE Ch. 10 - Prob. 83RE Ch. 10 - Prob. 84RE Ch. 10 - Prob. 85RE Ch. 10 - Prob. 86RE Ch. 10 - Prob. 87RE Ch. 10 - Prob. 88RE Ch. 10 - Prob. 89RE Ch. 10 - Prob. 90RE Ch. 10 - Prob. 91RE Ch. 10 - Prob. 92RE Ch. 10 - Prob. 93RE Ch. 10 - Prob. 94RE Ch. 10 - Prob. 95RE Ch. 10 - Prob. 1PT Ch. 10 - In Problems 2–5, sketch the graphs of the given...Ch. 10 - Prob. 3PT Ch. 10 - Prob. 4PT Ch. 10 - Prob. 5PT Ch. 10 - Prob. 6PT Ch. 10 - Prob. 7PT Ch. 10 - Prob. 8PT Ch. 10 - Prob. 9PT Ch. 10 - Prob. 10PT

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The amplitude and period of the function y = − 1 2 cos 2 3 x and sketch the graph.

Videos

The amplitude and period of the function y=−12cos23x and sketch the graph.

Want to see the full answer?

Chapter 10 Solutions