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a.
Sketch a
a.
![Check Mark](/static/check-mark.png)
Answer to Problem 3P
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=[0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5]; y=[21.1 23.6 24.5 21.7 17.5 12.0 5.6 2.2 1.0 3.5 7.6 13.2 18.4 23.0 25.1]; scatter(t,y,'linewidth',1.25'); set(gca,'Linewidth',1.2,'Fontsize',12); xlabel('t'); ylabel('y') 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.
![Check Mark](/static/check-mark.png)
Answer to Problem 3P
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=[0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5]; y=[21.1 23.6 24.5 21.7 17.5 12.0 5.6 2.2 1.0 3.5 7.6 13.2 18.4 23.0 25.1]; 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.
![Check Mark](/static/check-mark.png)
Answer to Problem 3P
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=[0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5]; y=[21.1 23.6 24.5 21.7 17.5 12.0 5.6 2.2 1.0 3.5 7.6 13.2 18.4 23.0 25.1]; 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'); ylabel('y') 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.
![Check Mark](/static/check-mark.png)
Answer to Problem 3P
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=[0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5]; y=[21.1 23.6 24.5 21.7 17.5 12.0 5.6 2.2 1.0 3.5 7.6 13.2 18.4 23.0 25.1]; 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;
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.
e.
Compare the results from part (b) and (c).
e.
![Check Mark](/static/check-mark.png)
Answer to Problem 3P
Using reduction relation, the graph of the given data is,
Explanation of Solution
Given: the reduction formula,
Calculation:
As we can see in part (d) the sine function is,
Where,
Then rewrite the function as,
Simplify the above function and sketch a graph.
Program:
clc clear close all t=[0 25 50 75 100 125 150 175 200 225 250 275 300 325 350]; y=[190 175 155 125 110 95 105 120 140 165 185 200 195 185 165]; 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)-pi/2))+b; scatter(t,y,'linewidth',1.25'); hold on plot(t,f,'linewidth',1.25'); set(gca,'linewidth',1.2,'fontsize',12); xlabel('t'); ylabel('y') axis square axis tight
Query:
- First, we have defined the given data sets.
- Then calculate the value of b, a, w, and c.
- Then using reduction relation redefine the function.
- Sketch a graph.
Chapter 5 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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