Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015
Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015
1st Edition
ISBN: 9781680331165
Author: HOUGHTON MIFFLIN HARCOURT
Publisher: Houghton Mifflin Harcourt
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Question
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Chapter 9.6, Problem 29E
To determine

To find: A sine and cosine function for the given sinusoid.

Expert Solution & Answer
Check Mark

Answer to Problem 29E

  y=2.5cos(4t)+5.5 or y=2.5sin(4tπ2)+5.5 .

Explanation of Solution

Given information:

During one cycle, a sinusoid has minimum at (π2,3) and maximum at (π4,8) .

Calculation:

As per the given information −

During one cycle, a sinusoid has minimum at (π2,3) and maximum at (π4,8) .

Step 1: Find the maximum and minimum value.

Here, maximum value is 8 and minimum value is 3 .

Step 2: Identify the vertical shift k .

The value of k is the mean of maximum and minimum value, i.e.

  k=8+32=5.5

Step 3: Find the amplitude and period.

  |a|=Maximum valueMinimum value2=832=2.5Since graph is not a reflection, a>0a=2.5

Since the function goes from maximum to minimum during period (π4,π2) . So, function again will go from minimum to maximum during the period (π2,3π4) . Thus, function is repeating itself every π2 period. Therefore, period of the function would be π2 .

  i.eπ2=2πbb=4

Also at t=0 , function would be at its minimum value. So, cosine function reflected across x axis can be taken as model.

Step 5 : The function graph would be given as −

  y=2.5cos(4t)+5.5

Hence, desired function of the given graph is y=2.5cos(4t)+5.5 .

  Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015, Chapter 9.6, Problem 29E , additional homework tip  1

Taking sine as model function:

When sine is taken as model function then function should be shifted π8 units rightward.

  So, y=2.5sin[4(tπ8)]+5.5y=2.5sin(4tπ2)+5.5

  Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015, Chapter 9.6, Problem 29E , additional homework tip  2

Hence, desired model functions would be y=2.5cos(4t)+5.5 or y=2.5sin(4tπ2)+5.5 .

Chapter 9 Solutions

Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015

Ch. 9.1 - Prob. 11ECh. 9.1 - Prob. 12ECh. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Prob. 15ECh. 9.1 - Prob. 16ECh. 9.1 - Prob. 17ECh. 9.1 - Prob. 18ECh. 9.1 - Prob. 19ECh. 9.1 - Prob. 20ECh. 9.1 - Prob. 21ECh. 9.1 - Prob. 22ECh. 9.1 - Prob. 23ECh. 9.1 - Prob. 24ECh. 9.1 - Prob. 25ECh. 9.1 - Prob. 26ECh. 9.1 - Prob. 27ECh. 9.1 - Prob. 28ECh. 9.1 - Prob. 29ECh. 9.1 - Prob. 30ECh. 9.1 - Prob. 31ECh. 9.1 - Prob. 32ECh. 9.1 - Prob. 33ECh. 9.1 - Prob. 34ECh. 9.1 - Prob. 35ECh. 9.1 - Prob. 36ECh. 9.1 - Prob. 37ECh. 9.1 - Prob. 38ECh. 9.1 - Prob. 39ECh. 9.1 - Prob. 40ECh. 9.1 - Prob. 41ECh. 9.1 - Prob. 42ECh. 9.1 - Prob. 43ECh. 9.1 - Prob. 44ECh. 9.1 - Prob. 45ECh. 9.1 - Prob. 46ECh. 9.1 - Prob. 47ECh. 9.1 - Prob. 48ECh. 9.1 - Prob. 49ECh. 9.1 - Prob. 50ECh. 9.1 - Prob. 51ECh. 9.1 - Prob. 52ECh. 9.1 - Prob. 53ECh. 9.1 - Prob. 54ECh. 9.1 - Prob. 55ECh. 9.1 - Prob. 56ECh. 9.1 - Prob. 57ECh. 9.1 - Prob. 58ECh. 9.1 - Prob. 59ECh. 9.2 - Prob. 1ECh. 9.2 - Prob. 2ECh. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - 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Prob. 33ECh. 9.7 - Prob. 34ECh. 9.7 - Prob. 35ECh. 9.7 - Prob. 36ECh. 9.7 - Prob. 37ECh. 9.7 - Prob. 38ECh. 9.7 - Prob. 39ECh. 9.7 - Prob. 40ECh. 9.7 - Prob. 41ECh. 9.7 - Prob. 42ECh. 9.7 - Prob. 43ECh. 9.8 - Prob. 1ECh. 9.8 - Prob. 2ECh. 9.8 - Prob. 3ECh. 9.8 - Prob. 4ECh. 9.8 - Prob. 5ECh. 9.8 - Prob. 6ECh. 9.8 - Prob. 7ECh. 9.8 - Prob. 8ECh. 9.8 - Prob. 9ECh. 9.8 - Prob. 10ECh. 9.8 - Prob. 11ECh. 9.8 - Prob. 12ECh. 9.8 - Prob. 13ECh. 9.8 - Prob. 14ECh. 9.8 - Prob. 15ECh. 9.8 - Prob. 16ECh. 9.8 - Prob. 17ECh. 9.8 - Prob. 18ECh. 9.8 - Prob. 19ECh. 9.8 - Prob. 20ECh. 9.8 - Prob. 21ECh. 9.8 - Prob. 22ECh. 9.8 - Prob. 23ECh. 9.8 - Prob. 24ECh. 9.8 - Prob. 25ECh. 9.8 - Prob. 26ECh. 9.8 - Prob. 27ECh. 9.8 - Prob. 28ECh. 9.8 - Prob. 29ECh. 9.8 - Prob. 30ECh. 9.8 - Prob. 31ECh. 9.8 - Prob. 32ECh. 9.8 - Prob. 33ECh. 9.8 - Prob. 34ECh. 9.8 - Prob. 35ECh. 9.8 - Prob. 36ECh. 9.8 - Prob. 37ECh. 9.8 - Prob. 38ECh. 9.8 - Prob. 39ECh. 9.8 - Prob. 40ECh. 9.8 - Prob. 41ECh. 9.8 - Prob. 42ECh. 9.8 - Prob. 43ECh. 9 - 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