
Concept explainers
a.
Sketch a
a.

Answer to Problem 5P
The scatter plot is
Explanation of Solution
Given: A set of the data is,
Calculation:
Let’s take a given data set sketch a scatter plot using MATLAB.
The function is using in the MATLAB to sketch a scatter plot is,
Program:
clc clear close all t=[1 2 3 4 5 6 7 8 9 10 11 12]; y=[40.0 43.1 54.6 64.2 73.8 81.8 85.8 83.9 76.9 66.8 55.5 44.5]; scatter(t,y,'linewidth',1.25'); set(gca,'Linewidth',1.2,'Fontsize',12); xlabel('t (Month)'); ylabel('Average temperature (^{\circ}F)') axis square axis tight
Query:
- First, we have defined the given data sets.
- Then using a function “scatter (t, y)” sketch a scatter plot.
b.
Calculate the cosine function using given data set.
b.

Answer to Problem 5P
The cosine function is,
Explanation of Solution
Given: A set of the data is,
Calculation:
First, we have to write a general equation of the cosine function,
Then, calculate the vertical shifting as,
Calculate the amplitude as,
Then, Calculate the phase shift as,
The value of c is,
Put all the value into the equation (1) then,
Program:
clc clear close all t=[1 2 3 4 5 6 7 8 9 10 11 12]; y=[40.0 43.1 54.6 64.2 73.8 81.8 85.8 83.9 76.9 66.8 55.5 44.5]; b=(1/2)*(max(y)+min(y)); a=(1/2)*(max(y)-min(y)); w=2*pi/max(t); idx=find(y==max(y)); c=t(idx); f=(a*cos(w*(t-c)))+b;
Query:
- First, we have defined the given data sets.
- Then calculate the value of b, a, w, and c.
- Put all the values into the equation of cosine function and get the solution.
c.
Sketch a graph of the function which is found in part (b).
c.

Answer to Problem 5P
The solution is,
Explanation of Solution
Given: A set of the data is,
Calculation:
Sketch a graph of the cosine function in MATLAB using function “plot (f, t)”.
The function is found in part (b) is,
Program:
clc clear close all t=[1 2 3 4 5 6 7 8 9 10 11 12]; y=[40.0 43.1 54.6 64.2 73.8 81.8 85.8 83.9 76.9 66.8 55.5 44.5]; b=(1/2)*(max(y)+min(y)); a=(1/2)*(max(y)-min(y)); w=2*pi/max(t); idx=find(y==max(y)); c=t(idx); f=(a*cos(w*(t-c)))+b; scatter(t,y,'linewidth',1.25'); hold on plot(t,f,'linewidth',1.25'); set(gca,'Linewidth',1.2,'Fontsize',12); xlabel('t (Month)'); ylabel('Average temperature (^{\circ}F)') axis square axis tight
Query:
- First, we have defined the given data sets.
- Then calculate the value of b, a, w, and c.
- Put all the values into the equation of cosine function and get the solution.
- Then sketch a graph.
d.
Calculate the sine function using given data set.
d.

Answer to Problem 5P
The cosine function is,
And the best fitting curve is,
Explanation of Solution
Given: A set of the data is,
Calculation:
First, we have to write a general equation of the cosine function,
Then, calculate the vertical shifting as,
Calculate the amplitude as,
Then, Calculate the phase shift as,
The value of c is,
Put all the value into the equation (1) then,
Program:
clc clear close all t=[1 2 3 4 5 6 7 8 9 10 11 12]; y=[40.0 43.1 54.6 64.2 73.8 81.8 85.8 83.9 76.9 66.8 55.5 44.5]; b=(1/2)*(max(y)+min(y)); a=(1/2)*(max(y)-min(y)); w=2*pi/max(t); idx=find(y==max(y)); c=t(idx); f=(a*sin(w*(t+c)))+b; scatter(t,y,'linewidth',1.25'); hold on plot(t,f,'linewidth',1.25'); set(gca,'Linewidth',1.2,'Fontsize',12); xlabel('t (Month)'); ylabel('Average temperature (^{\circ}F)') axis square axis tight
Query:
- First, we have defined the given data sets.
- Then calculate the value of b, a, w, and c.
- Put all the values into the equation of cosine function and get the solution.
- Then sketch a best fitting curve with the scatter plot.
Chapter 5 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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