Precalculus: Mathematics for Calculus - 6th Edition

6th Edition

ISBN: 9780840068071

Author: Stewart, James, Redlin, Lothar, Watson, Saleem

Publisher: Cengage Learning

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Question

Chapter 5, Problem 9P

To determine

Sketch a scatter plot for the given data set.

Expert Solution

Answer to Problem 9P

The scatter plot is

Precalculus: Mathematics for Calculus - 6th Edition, Chapter 5, Problem 9P , additional homework tip 1

Explanation of Solution

Given: A set of the data is,

YearSunspotsYearSunspots1975161990143197613199114619772819929419789319935519791551994301980155199518198114019969198211619972119836719986419844619999319851820001191986132001111198729200210419881002003641989158200440

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,

scatter(t,y)

Program:

clc
clear
close all
t=1975:1:2004;
y=[16 13 28 93 155 155 140 116 67 46 18 13 29 100 158 ...
    143 146 94 55 30 18 9 21 64 93 119 111 104 64 40];
scatter(t,y,'linewidth',1.25');
set(gca,'Linewidth',1.2,'Fontsize',12);
xlabel('t (Month)');
ylabel('sunspots')
axis square
axis tight

Query:

First, we have defined the given data sets.
Then using a function “scatter (t, y)” sketch a scatter plot.

To determine

Calculate the cosine function using given data set.

Expert Solution

Answer to Problem 9P

The cosine function is,

y=22.9×cos(0.5236(t−7))+62.9

Explanation of Solution

Given: A set of the data is,

Calculation:

First, we have to write a general equation of the cosine function,

y=acos(w(t−c))+b ......(1)

Then, calculate the vertical shifting as,

b=12(max value(y) + min value(y))=83.5

Calculate the amplitude as,

a=12(max value(y) - min value(y))=74.5

Then, Calculate the phase shift as,

w=2πperod=0.2094

The value of c is,

c=time period at which y value is maximum=1989

Put all the value into the equation (1) then,

y=74.5×cos(0.2094(t−1989))+83.5

Program:

clc
clear
close all
t=1975:1:2004;
y=[16 13 28 93 155 155 140 116 67 46 18 13 29 100 158 ...
    143 146 94 55 30 18 9 21 64 93 119 111 104 64 40];
b=(1/2)*(max(y)+min(y));
a=(1/2)*(max(y)-min(y));
w=2*pi/30;
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.

To determine

Sketch a graph of the function which is found in part (b).

Expert Solution

Answer to Problem 9P

The solution is,

Precalculus: Mathematics for Calculus - 6th Edition, Chapter 5, Problem 9P , additional homework tip 2

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,

y=22.9×cos(0.5236(t−7))+62.9

Program:

clc
clear
close all
t=1975:1:2004;
y=[16 13 28 93 155 155 140 116 67 46 18 13 29 100 158 ...
    143 146 94 55 30 18 9 21 64 93 119 111 104 64 40];
b=(1/2)*(max(y)+min(y));
a=(1/2)*(max(y)-min(y));
w=2*pi/30;
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('sunspots')
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.

To determine

Calculate the sine function using given data set.

Expert Solution

Answer to Problem 9P

The cosine function is,

y=74.5×sin(0.2094(t+1989))+83.5

And the best fitting curve is,

Precalculus: Mathematics for Calculus - 6th Edition, Chapter 5, Problem 9P , additional homework tip 3

Explanation of Solution

Given: A set of the data is,

Calculation:

First, we have to write a general equation of the cosine function,

y=asin(w(t−c))+b ......(1)

Then, calculate the vertical shifting as,

b=12(max value(y) + min value(y))=83.5

Calculate the amplitude as,

a=12(max value(y) - min value(y))=74.5

Then, Calculate the phase shift as,

w=2πperod=0.2094

The value of c is,

c=time period at which y value is maximum=1989

Put all the value into the equation (1) then,

y=74.5×sin(0.2094(t+1989))+83.5

Program:

clc
clear
close all
t=1975:1:2004;
y=[16 13 28 93 155 155 140 116 67 46 18 13 29 100 158 ...
    143 146 94 55 30 18 9 21 64 93 119 111 104 64 40];
b=(1/2)*(max(y)+min(y));
a=(1/2)*(max(y)-min(y));
w=2*pi/30;
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('sunspots')
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, Problem 8P

Chapter 6.1, Problem 1E

Chapter 5 Solutions

Precalculus: Mathematics for Calculus - 6th Edition

Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E

Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - Prob. 49E Ch. 5.1 - Prob. 50E Ch. 5.1 - Prob. 51E Ch. 5.1 - Prob. 52E Ch. 5.1 - Prob. 53E Ch. 5.1 - Prob. 54E Ch. 5.1 - Prob. 55E Ch. 5.1 - Prob. 56E Ch. 5.1 - Prob. 57E Ch. 5.1 - Prob. 58E Ch. 5.2 - Let P(x, y) be the terminal point on the unit...Ch. 5.2 - If P(x, y) is on the unit circle, then x2 + y2 =...Ch. 5.2 - Prob. 3E Ch. 5.2 - Prob. 4E Ch. 5.2 - Prob. 5E Ch. 5.2 - Prob. 6E Ch. 5.2 - Prob. 7E Ch. 5.2 - Prob. 8E Ch. 5.2 - Prob. 9E Ch. 5.2 - Prob. 10E Ch. 5.2 - Prob. 11E Ch. 5.2 - Prob. 12E Ch. 5.2 - Prob. 13E Ch. 5.2 - Prob. 14E Ch. 5.2 - Prob. 15E Ch. 5.2 - Prob. 16E Ch. 5.2 - Prob. 17E Ch. 5.2 - Prob. 18E Ch. 5.2 - Prob. 19E Ch. 5.2 - Prob. 20E Ch. 5.2 - Prob. 21E Ch. 5.2 - Prob. 22E Ch. 5.2 - Prob. 23E Ch. 5.2 - Prob. 24E Ch. 5.2 - Prob. 25E Ch. 5.2 - Prob. 26E Ch. 5.2 - Prob. 27E Ch. 5.2 - Prob. 28E Ch. 5.2 - Prob. 29E Ch. 5.2 - Prob. 30E Ch. 5.2 - Prob. 31E Ch. 5.2 - Prob. 32E Ch. 5.2 - Prob. 33E Ch. 5.2 - Prob. 34E Ch. 5.2 - Prob. 35E Ch. 5.2 - Prob. 36E Ch. 5.2 - Prob. 37E Ch. 5.2 - Prob. 38E Ch. 5.2 - Prob. 39E Ch. 5.2 - Prob. 40E Ch. 5.2 - Prob. 41E Ch. 5.2 - Prob. 42E Ch. 5.2 - Prob. 43E Ch. 5.2 - Prob. 44E Ch. 5.2 - Prob. 45E Ch. 5.2 - Prob. 46E Ch. 5.2 - Prob. 47E Ch. 5.2 - Prob. 48E Ch. 5.2 - Prob. 49E Ch. 5.2 - Prob. 50E Ch. 5.2 - 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The cancellation property sin1(sin x) = x is valid...Ch. 5.5 - Prob. 3E Ch. 5.5 - Prob. 4E Ch. 5.5 - Prob. 5E Ch. 5.5 - Prob. 6E Ch. 5.5 - Prob. 7E Ch. 5.5 - Prob. 8E Ch. 5.5 - Prob. 9E Ch. 5.5 - Prob. 10E Ch. 5.5 - Prob. 11E Ch. 5.5 - Prob. 12E Ch. 5.5 - Prob. 13E Ch. 5.5 - Prob. 14E Ch. 5.5 - Prob. 15E Ch. 5.5 - Prob. 16E Ch. 5.5 - Prob. 17E Ch. 5.5 - Prob. 18E Ch. 5.5 - Prob. 19E Ch. 5.5 - Prob. 20E Ch. 5.5 - Prob. 21E Ch. 5.5 - Prob. 22E Ch. 5.5 - Prob. 23E Ch. 5.5 - Prob. 24E Ch. 5.5 - Prob. 25E Ch. 5.5 - Prob. 26E Ch. 5.5 - Prob. 27E Ch. 5.5 - Prob. 28E Ch. 5.5 - Prob. 29E Ch. 5.5 - Prob. 30E Ch. 5.5 - Prob. 31E Ch. 5.5 - Prob. 32E Ch. 5.5 - Prob. 33E Ch. 5.5 - Prob. 34E Ch. 5.5 - Prob. 35E Ch. 5.5 - Prob. 36E Ch. 5.5 - Prob. 37E Ch. 5.5 - Prob. 38E Ch. 5.5 - Prob. 39E Ch. 5.5 - Prob. 40E Ch. 5.5 - Prob. 41E Ch. 5.5 - Prob. 42E Ch. 5.5 - Prob. 43E Ch. 5.5 - Prob. 44E Ch. 5.5 - Prob. 45E Ch. 5.5 - Prob. 46E Ch. 5.5 - Prob. 47E Ch. 5.6 - For an object in simple harmonic motion with...Ch. 5.6 - For an object in damped harmonic motion with...Ch. 5.6 - Prob. 3E Ch. 5.6 - Prob. 4E Ch. 5.6 - Prob. 5E Ch. 5.6 - Prob. 6E Ch. 5.6 - Prob. 7E Ch. 5.6 - Prob. 8E Ch. 5.6 - Prob. 9E Ch. 5.6 - Prob. 10E Ch. 5.6 - Prob. 11E Ch. 5.6 - Prob. 12E Ch. 5.6 - Prob. 13E Ch. 5.6 - Prob. 14E Ch. 5.6 - Prob. 15E Ch. 5.6 - Prob. 16E Ch. 5.6 - Prob. 17E Ch. 5.6 - Prob. 18E Ch. 5.6 - Prob. 19E Ch. 5.6 - Prob. 20E Ch. 5.6 - Prob. 21E Ch. 5.6 - Prob. 22E Ch. 5.6 - Prob. 23E Ch. 5.6 - Prob. 24E Ch. 5.6 - Prob. 25E Ch. 5.6 - Prob. 26E Ch. 5.6 - A Bobbing Cork A cork floating in a lake is...Ch. 5.6 - FM Radio Signals The carrier wave for an FM radio...Ch. 5.6 - Blood Pressure Each time your heart beats, your...Ch. 5.6 - Predator Population Model In a predator/prey...Ch. 5.6 - Prob. 31E Ch. 5.6 - Tides The graph shows the variation of the water...Ch. 5.6 - Tides The Bay of Fundy in Nova Scotia has the...Ch. 5.6 - Prob. 34E Ch. 5.6 - Prob. 35E Ch. 5.6 - Prob. 36E Ch. 5.6 - Ferris Wheel A Ferris wheel has a radius of 10 m,...Ch. 5.6 - Cock Pendulum The pendulum in a grandfather clock...Ch. 5.6 - Variable Stars The variable star Zeta Gemini has a...Ch. 5.6 - Variable Stars Astronomers believe that the radius...Ch. 5.6 - Biological Clocks Circadian rhythms are biological...Ch. 5.6 - Electric Generator The armature in an electric...Ch. 5.6 - Electric Generator The graph shows an oscilloscope...Ch. 5.6 - Doppler Effect When a car with its horn blowing...Ch. 5.6 - Motion of a Building A strong gust of wind strikes...Ch. 5.6 - Shock Absorber When a car hits a certain bump on...Ch. 5.6 - Tuning Fork A tuning fork is struck and oscillates...Ch. 5.6 - Guitar String A guitar string is pulled at point P...Ch. 5 - Prob. 1RCC Ch. 5 - Prob. 2RCC Ch. 5 - Prob. 3RCC Ch. 5 - Prob. 4RCC Ch. 5 - Prob. 5RCC Ch. 5 - Prob. 6RCC Ch. 5 - Prob. 7RCC Ch. 5 - Prob. 8RCC Ch. 5 - Prob. 9RCC Ch. 5 - Prob. 10RCC Ch. 5 - Prob. 11RCC Ch. 5 - Prob. 12RCC Ch. 5 - Prob. 1RE Ch. 5 - Prob. 2RE Ch. 5 - Prob. 3RE Ch. 5 - Prob. 4RE Ch. 5 - Prob. 5RE Ch. 5 - 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