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
Chapter 9.6, Problem 29E
To determine
To find: A sine and cosine function for the given sinusoid.
Expert Solution & Answer
Answer to Problem 29E
y=−2.5cos(4t)+5.5 or y=2.5sin(4t−π2)+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 value−Minimum value2=8−32=2.5Since graph is not a reflection, a>0⇒a=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.e. π2=2πb⇒b=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 .
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(t−π8)]+5.5⇒y=2.5sin(4t−π2)+5.5
Hence, desired model functions would be y=−2.5cos(4t)+5.5 or y=2.5sin(4t−π2)+5.5 .
Chapter 9 Solutions
Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015
Ch. 9.1 - Prob. 1ECh. 9.1 - Prob. 2ECh. 9.1 - Prob. 3ECh. 9.1 - Prob. 4ECh. 9.1 - Prob. 5ECh. 9.1 - Prob. 6ECh. 9.1 - Prob. 7ECh. 9.1 - Prob. 8ECh. 9.1 - Prob. 9ECh. 9.1 - Prob. 10E
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