This document describes 65 tutorials that provide examples of constructing tables and graphs for cosecant functions. Each tutorial examines a cosecant function of the form y = csc(ax + b) or y = a * csc(bx + c) + d with different values for the variables a, b, c, and d. The tutorials demonstrate how changing the values of these variables affects the shape of the cosecant function graph and its table of values.
SAMPLE QUESTIONExercise 1 Consider the functionf (x,C).docxagnesdcarey33086
SAMPLE QUESTION:
Exercise 1: Consider the function
f (x,C)=
sin(C x)
Cx
(a) Create a vector x with 100 elements from -3*pi to 3*pi. Write f as an inline or anonymous function
and generate the vectors y1 = f(x,C1), y2 = f(x,C2) and y3 = f(x,C3), where C1 = 1, C2 = 2 and
C3 = 3. Make sure you suppress the output of x and y's vectors. Plot the function f (for the three
C's above), name the axis, give a title to the plot and include a legend to identify the plots. Add a
grid to the plot.
(b) Without using inline or anonymous functions write a function+function structure m-file that does
the same job as in part (a)
SAMPLE LAB WRITEUP:
MAT 275 MATLAB LAB 1 NAME: __________________________
LAB DAY and TIME:______________
Instructor: _______________________
Exercise 1
(a)
x = linspace(-3*pi,3*pi); % generating x vector - default value for number
% of pts linspace is 100
f= @(x,C) sin(C*x)./(C*x) % C will be just a constant, no need for ".*"
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % supressing the y's
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
Command window output:
f =
@(x,C)sin(C*x)./(C*x)
C1 =
1
C2 =
2
C3 =
3
(b)
M-file of structure function+function
function ex1
x = linspace(-3*pi,3*pi); % generating x vector - default value for number
% of pts linspace is 100
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % function f is defined below
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
end
function y = f(x,C)
y = sin(C*x)./(C*x);
end
Command window output:
C1 =
1
C2 =
2
C3 =
3
Joe Bob
Mon lab: 4:30-6:50
Lab 3
Exercise 1
(a) Create function M-file for banded LU factorization
function [L,U] = luband(A,p)
% LUBAND Banded LU factorization
% Adaptation to LUFACT
% Input:
% A diagonally dominant square matrix
% Output:
% L,U unit lower triangular and upper triangular such that LU=A
n = length(A);
L = eye(n); % ones on diagonal
% Gaussian Elimination
for j = 1:n-1
a = min(j+p.
M166Calculus” ProjectDue Wednesday, December 9, 2015PROJ.docxinfantsuk
M166
“Calculus” Project
Due: Wednesday, December 9, 2015
PROJECT WORTH 50 POINTS –
1) NO LATE SUBMISSIONS WILL BE ACCEPTED
2) COMPLETED PROJECTS NEED TO BE LEGIBLE
I. Computing Derivatives (slope of curve at a point) of polynomial functions.
For each of the following functions in a.-e. below perform the following three steps:
1. compute the difference quotient
2. simplify expression from part 1. such that h has been canceled from the denominator
3. substitute and simplify
a.
b.
c.
d.
e. consider , using the results from parts a. through d.,
f. find a general formula for (steps 1 through 3 performed).
II. Show that
Consider the unit circle with in standard position in QI.
a. show that the area of the right triangle (see diagram) is
b. show that the area of the sector (see diagram) is
c. show that the area of the acute triangle (see diagram)
d. set up the inequality
e. multiply the inequality in part d. by . (direction of inequalities is unchanged)
f. take the reciprocal of each term from part e. The direction of the inequality must be reversed because .
g. plug in 0 for for only. The result should be
III. Show that
a. multiply by
b. use trigonometric identity to rewrite the numerator of the expression in part a. in terms of
c. factor the expression in part b. with one factor equal to . (find remaining factor).
d. use the fact that and substitute in the second factor (result is 0)
IV. Show that derivative of
a. find the difference quotient for
(use sum angle formula )
b. factor out of the two terms in the numerator with in part a
c. split up the expression in part b with each term over the denominator h
d. use identities to simplify part c. to
Thus you have shown that if .
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MATH133: Unit 3 Individual Project 2B Student Answer Form
Name (Required): ____Michael Magro_________________________
Please show all work details with answers, insert the graph, and provide answers to all the critical thinking questions on this form for the Unit 3 IP assignment.
A version of Amdah ...
SAMPLE QUESTIONExercise 1 Consider the functionf (x,C).docxagnesdcarey33086
SAMPLE QUESTION:
Exercise 1: Consider the function
f (x,C)=
sin(C x)
Cx
(a) Create a vector x with 100 elements from -3*pi to 3*pi. Write f as an inline or anonymous function
and generate the vectors y1 = f(x,C1), y2 = f(x,C2) and y3 = f(x,C3), where C1 = 1, C2 = 2 and
C3 = 3. Make sure you suppress the output of x and y's vectors. Plot the function f (for the three
C's above), name the axis, give a title to the plot and include a legend to identify the plots. Add a
grid to the plot.
(b) Without using inline or anonymous functions write a function+function structure m-file that does
the same job as in part (a)
SAMPLE LAB WRITEUP:
MAT 275 MATLAB LAB 1 NAME: __________________________
LAB DAY and TIME:______________
Instructor: _______________________
Exercise 1
(a)
x = linspace(-3*pi,3*pi); % generating x vector - default value for number
% of pts linspace is 100
f= @(x,C) sin(C*x)./(C*x) % C will be just a constant, no need for ".*"
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % supressing the y's
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
Command window output:
f =
@(x,C)sin(C*x)./(C*x)
C1 =
1
C2 =
2
C3 =
3
(b)
M-file of structure function+function
function ex1
x = linspace(-3*pi,3*pi); % generating x vector - default value for number
% of pts linspace is 100
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % function f is defined below
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
end
function y = f(x,C)
y = sin(C*x)./(C*x);
end
Command window output:
C1 =
1
C2 =
2
C3 =
3
Joe Bob
Mon lab: 4:30-6:50
Lab 3
Exercise 1
(a) Create function M-file for banded LU factorization
function [L,U] = luband(A,p)
% LUBAND Banded LU factorization
% Adaptation to LUFACT
% Input:
% A diagonally dominant square matrix
% Output:
% L,U unit lower triangular and upper triangular such that LU=A
n = length(A);
L = eye(n); % ones on diagonal
% Gaussian Elimination
for j = 1:n-1
a = min(j+p.
M166Calculus” ProjectDue Wednesday, December 9, 2015PROJ.docxinfantsuk
M166
“Calculus” Project
Due: Wednesday, December 9, 2015
PROJECT WORTH 50 POINTS –
1) NO LATE SUBMISSIONS WILL BE ACCEPTED
2) COMPLETED PROJECTS NEED TO BE LEGIBLE
I. Computing Derivatives (slope of curve at a point) of polynomial functions.
For each of the following functions in a.-e. below perform the following three steps:
1. compute the difference quotient
2. simplify expression from part 1. such that h has been canceled from the denominator
3. substitute and simplify
a.
b.
c.
d.
e. consider , using the results from parts a. through d.,
f. find a general formula for (steps 1 through 3 performed).
II. Show that
Consider the unit circle with in standard position in QI.
a. show that the area of the right triangle (see diagram) is
b. show that the area of the sector (see diagram) is
c. show that the area of the acute triangle (see diagram)
d. set up the inequality
e. multiply the inequality in part d. by . (direction of inequalities is unchanged)
f. take the reciprocal of each term from part e. The direction of the inequality must be reversed because .
g. plug in 0 for for only. The result should be
III. Show that
a. multiply by
b. use trigonometric identity to rewrite the numerator of the expression in part a. in terms of
c. factor the expression in part b. with one factor equal to . (find remaining factor).
d. use the fact that and substitute in the second factor (result is 0)
IV. Show that derivative of
a. find the difference quotient for
(use sum angle formula )
b. factor out of the two terms in the numerator with in part a
c. split up the expression in part b with each term over the denominator h
d. use identities to simplify part c. to
Thus you have shown that if .
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=
h
c
x
f
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b
ax
x
f
+
=
)
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c
bx
ax
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bx
ax
x
f
+
+
+
=
2
3
)
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(
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3
2
2
3
3
3
3
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MATH133: Unit 3 Individual Project 2B Student Answer Form
Name (Required): ____Michael Magro_________________________
Please show all work details with answers, insert the graph, and provide answers to all the critical thinking questions on this form for the Unit 3 IP assignment.
A version of Amdah ...
MATLAB sessions: Laboratory 2
MAT 275 Laboratory 2
Matrix Computations and Programming in MATLAB
In this laboratory session we will learn how to
1. Create and manipulate matrices and vectors.
2. Write simple programs in MATLAB
NOTE: For your lab write-up, follow the instructions of LAB1.
Matrices and Linear Algebra
⋆ Matrices can be constructed in MATLAB in different ways. For example the 3 × 3 matrix
A =
8 1 63 5 7
4 9 2
can be entered as
>> A=[8,1,6;3,5,7;4,9,2]
A =
8 1 6
3 5 7
4 9 2
or
>> A=[8,1,6;
3,5,7;
4,9,2]
A =
8 1 6
3 5 7
4 9 2
or defined as the concatenation of 3 rows
>> row1=[8,1,6]; row2=[3,5,7]; row3=[4,9,2]; A=[row1;row2;row3]
A =
8 1 6
3 5 7
4 9 2
or 3 columns
>> col1=[8;3;4]; col2=[1;5;9]; col3=[6;7;2]; A=[col1,col2,col3]
A =
8 1 6
3 5 7
4 9 2
Note the use of , and ;. Concatenated rows/columns must have the same length. Larger matrices can
be created from smaller ones in the same way:
c⃝2011 Stefania Tracogna, SoMSS, ASU
MATLAB sessions: Laboratory 2
>> C=[A,A] % Same as C=[A A]
C =
8 1 6 8 1 6
3 5 7 3 5 7
4 9 2 4 9 2
The matrix C has dimension 3 × 6 (“3 by 6”). On the other hand smaller matrices (submatrices) can
be extracted from any given matrix:
>> A(2,3) % coefficient of A in 2nd row, 3rd column
ans =
7
>> A(1,:) % 1st row of A
ans =
8 1 6
>> A(:,3) % 3rd column of A
ans =
6
7
2
>> A([1,3],[2,3]) % keep coefficients in rows 1 & 3 and columns 2 & 3
ans =
1 6
9 2
⋆ Some matrices are already predefined in MATLAB:
>> I=eye(3) % the Identity matrix
I =
1 0 0
0 1 0
0 0 1
>> magic(3)
ans =
8 1 6
3 5 7
4 9 2
(what is magic about this matrix?)
⋆ Matrices can be manipulated very easily in MATLAB (unlike Maple). Here are sample commands
to exercise with:
>> A=magic(3);
>> B=A’ % transpose of A, i.e, rows of B are columns of A
B =
8 3 4
1 5 9
6 7 2
>> A+B % sum of A and B
ans =
16 4 10
4 10 16
10 16 4
>> A*B % standard linear algebra matrix multiplication
ans =
101 71 53
c⃝2011 Stefania Tracogna, SoMSS, ASU
MATLAB sessions: Laboratory 2
71 83 71
53 71 101
>> A.*B % coefficient-wise multiplication
ans =
64 3 24
3 25 63
24 63 4
⋆ One MATLAB command is especially relevant when studying the solution of linear systems of dif-
ferentials equations: x=A\b determines the solution x = A−1b of the linear system Ax = b. Here is an
example:
>> A=magic(3);
>> z=[1,2,3]’ % same as z=[1;2;3]
z =
1
2
3
>> b=A*z
b =
28
34
28
>> x = A\b % solve the system Ax = b. Compare with the exact solution, z, defined above.
x =
1
2
3
>> y =inv(A)*b % solve the system using the inverse: less efficient and accurate
ans =
1.0000
2.0000
3.0000
Now let’s check for accuracy by evaluating the difference z − x and z − y. In exact arithmetic they
should both be zero since x, y and z all represent the solution to the system.
>> z - x % error for backslash command
ans =
0
0
0
>> z - y % error for inverse
ans =
1.0e-015 *
-0.4441
0
-0.88 ...
Lab 5 template Lab 5 - Your Name - MAT 275 Lab The M.docxsmile790243
Lab 5 template
%% Lab 5 - Your Name - MAT 275 Lab
% The Mass-Spring System
%% EX 1 10 pts
%A) 1 pts | short comment
%
%B) 2 pts | short comment
%
%C) 1 pts | short comment
%
%D) 1 pts
%E) 2 pts | List the first 3-4 t values either in decimal format or as
%fractions involving pi
%F) 3 pts | comments. | (1 pts for including two distinct graphs, each with y(t) and v(t) plotted)
%% EX 2 10 pts
%A) 5 pts
% add commands to LAB05ex1 to compute and plot E(t). Then use ylim([~,~]) to change the yaxis limits.
% You don't need to include this code but at least one plot of E(t) and a comment must be
% included!
%B) 2 pts | write out main steps here
% first differentiate E(t) with respect to t using the chain rule. Then
% make substitutions using the expression for omega0 and using the
% differential equation
%C) 3 pts | show plot and comment
%% EX 3 10 pts
%A) 3 pts | modify the system of equations in LAB05ex1a
% write the t value and either a) show correponding graph or b) explain given matlab
% commands
%B) 2 pts | write t value and max |V| value; include figure
%note: velocity magnitude is like absolute value!
%C) 3 pts | include 3 figures here + comments.
% use title('text') to attach a title to the figure
%D) 2 pts | What needs to happen (in terms of the characteristic equation)
%in order for there to be no oscillations? Impose a condition on the
%characteristic equation to find the critical c value. Write out main steps
%% EX4 10 pts
% A) 5 pts | include 1 figure and comment
%B) 2 pts
% again find dE/dt using the chain rule and make substitutions based on the
% differential equation. You should reach an expression for dE/dt which is
% in terms of y'
%C) 3 pts | include one figure and comment
Exercise (1):
function LAB05ex1
m = 1; % mass [kg]
k = 9; % spring constant [N/m]
omega0=sqrt(k/m);
y0=0.4; v0=0; % initial conditions
[t,Y]=ode45(@f,[0,10],[y0,v0],[],omega0); % solve for 0<t<10
y=Y(:,1); v=Y(:,2); % retrieve y, v from Y
figure(1); plot(t,y,'b+-',t,v,'ro-'); % time series for y and v
grid on;
%------------------------------------------------------
function dYdt= f(t,Y,omega0)
y = Y(1); v= Y(2);
dYdt = [v; -omega0^2*y];
Exercise (1a):
function LAB05ex1a
m = 1; % mass [kg]
k = 9; % spring constant [N/m]
c = 1; % friction coefficient [Ns/m]
omega0 = sqrt(k/m); p = c/(2*m);
y0 = 0.4; v0 = 0; % initial conditions
[t,Y]=ode45(@f,[0,10],[y0,v0],[],omega0,p); % solve for 0<t<10
y=Y(:,1); v=Y(:,2); % retrieve y, v from Y
figure(1); plot(t,y,'b+-',t,v,'ro-'); % time series for y and v
grid on
%------------------------------------------------------
function dYdt= f(t,Y,omega0,p)
y = Y(1); v= Y(2);
dYdt = [v; ?? ]; % fill-in dv/dt
More instructions for the l ...
A hands-on activity for explore a variety of math topics, including:
* Circumference and Diameter
* Linear functions and slope
* Ratios
* Data gathering and scatterplot
For more math resources, go to www.media4math.com.
Tutorials--The Language of Math--Variable Expressions--Multiplication and Sub...Media4math
This set of tutorials provides 32 examples of converting verbal expressions into variable expressions that involve multiplication and subtraction. Note: The download is a PPT file.
Tutorials--The Language of Math--Numerical Expressions--Multiplication Media4math
This set of tutorials provides 40 examples of converting verbal expressions into numerical expressions that involve multiplication. Note: The download is a PPT file.
Tutorials--The Language of Math--Numerical Expressions--Division Media4math
This set of tutorials provides 40 examples of converting verbal expressions into numerical expressions that involve division. Note: The download is a PPT file.
Tutorials--The Language of Math--Numerical Expressions--SubtractionMedia4math
This set of tutorials provides 40 examples of converting verbal expressions into numerical expressions that involve subtraction. Note: The download is a PPT file.
Tutorials--Language of Math--Numerical Expressions--AdditionMedia4math
This set of tutorials provides 40 examples of converting verbal expressions into numerical expressions that involve addition. The verbal expressions include these terms:
Plus
Increased by
In addition to
Added to
More than
In this issue of Math in the News we explore logarithmic functions to model the thawing of frozen turkeys. We look at USDA guidelines to determine data points and use a graphing calculator to create mathematical models.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
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http://sandymillin.wordpress.com/iateflwebinar2024
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2. Overview
This set of tutorials provides 65 examples of
cosecant functions in tabular and graph form.
3. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 01. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = csc(ax + b) with these characteristics: a = 1, b = 0.
4. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 02. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = csc(ax + b) with these characteristics: a > 1, b = 0.
5. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 03. In
this tutorial, construct a function table and graph for a cosecant function of
the form y = csc(ax + b) with these characteristics: a < -1, b = 0.
6. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 04. In
this tutorial, construct a function table and graph for a cosecant function of
the form y = csc(ax + b) with these characteristics: 0 < a < 1, b = 0.
7. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 05. In
this tutorial, construct a function table and graph for a cosecant function of
the form y = csc(ax + b) with these characteristics: -1 < a < 0, b = 0.
8. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 06. In
this tutorial, construct a function table and graph for a cosecant function of
the form y = csc(ax + b) with these characteristics: a = 1, b = π.
9. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 07. In
this tutorial, construct a function table and graph for a cosecant function of
the form y = csc(ax + b) with these characteristics: a > 1, b = π.
10. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 08. In
this tutorial, construct a function table and graph for a cosecant function of
the form y = csc(ax + b) with these characteristics: a < -1, b = π.
11. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 09. In this
tutorial, construct a function table and graph for a cosecant function of the
form y = csc(ax + b) with these characteristics: 0 < a < 1, b = π.
12. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 10. In this
tutorial, construct a function table and graph for a cosecant function of the
form y = csc(ax + b) with these characteristics: -1 < a < 0, b = π.
13. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 11. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = csc(ax + b) with these characteristics: a = 1, b = π/2.
14. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 12. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = csc(ax + b) with these characteristics: a > 1, b = π/2.
15. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 13. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = csc(ax + b) with these characteristics: a < -1, b = π/2.
16. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 14. In this
tutorial, construct a function table and graph for a cosecant function of the
form y = csc(ax + b) with these characteristics: 0 < a < 1, b = π/2.
17. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 15. In
this tutorial, construct a function table and graph for a cosecant function of
the form y = csc(ax + b) with these characteristics: -1 < a < 0, b = π/2.
18. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 16. In this
tutorial, construct a function table and graph for a cosecant function of the
form y = csc(ax + b) + c with these characteristics: a = 1, b = 0, c = 1.
19. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 17. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = csc(ax + b) + c with these characteristics: a > 1, b = 0, c = 1.
20. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 18. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = csc(ax + b) + c with these characteristics: a < -1, b = 0, c = 1.
21. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 19. In this
tutorial, construct a function table and graph for a cosecant function of the
form y = csc(ax + b) + c with these characteristics: 0 < a < 1, b = 0, c = 1.
22. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 20. In this
tutorial, construct a function table and graph for a cosecant function of the
form y = csc(ax + b) + c with these characteristics: -1 < a < 0, b = 0, c = 1.
23. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 21. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = csc(ax + b) + c with these characteristics: a = 1, b = π, c = 1.
24. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 22. In this
tutorial, construct a function table and graph for a cosecant function of the
form y = csc(ax + b) + c with these characteristics: a > 1, b = π, c = 1.
25. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 23. In this
tutorial, construct a function table and graph for a cosecant function of the
form y = csc(ax + b) + c with these characteristics: a < -1, b = π, c = 1.
26. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 24. In this
tutorial, construct a function table and graph for a cosecant function of the
form y = csc(ax + b) + c with these characteristics: 0 < a < 1, b = π, c = 1.
27. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 25. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = csc(ax + b) + c with these characteristics: -1 < a < 0, b = π, c = 1.
28. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 26. In this
tutorial, construct a function table and graph for a cosecant function of the
form y = csc(ax + b) + c with these characteristics: a = 1, b = π/2, c = 1.
29. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 27. In this
tutorial, construct a function table and graph for a cosecant function of the
form y = csc(ax + b) + c with these characteristics: a > 1, b = π/2, c = 1.
30. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 28. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = csc(ax + b) + c with these characteristics: a < -1, b = π/2, c = 1.
31. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 29. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = csc(ax + b) + c with these characteristics: 0 < a < 1, b = π/2, c = 1.
32. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 30. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = csc(ax + b) + c with these characteristics: -1 < a < 0, b = π/2, c = 1.
33. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 31. In this
tutorial, construct a function table and graph for a cosecant function of the form y
= csc(ax + b) + c with these characteristics: a = 1, b = 0, c = -1.
34. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 32. In this
tutorial, construct a function table and graph for a cosecant function of the form y
= csc(ax + b) + c with these characteristics: a > 1, b = 0, c = -1.
35. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 33. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = csc(ax + b) + c with these characteristics: a < -1, b = 0, c = -1.
36. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 34. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = csc(ax + b) + c with these characteristics: 0 < a < 1, b = 0, c = -1.
37. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 35. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = csc(ax + b) + c with these characteristics: -1 < a < 0, b = 0, c = -1.
38. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 36. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = csc(ax + b) + c with these characteristics: a = 1, b = π, c = -1.
39. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 37. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = csc(ax + b) + c with these characteristics: a > 1, b = π, c = -1.
40. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 38. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = csc(ax + b) + c with these characteristics: a < -1, b = π, c = -1.
41. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 39. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = csc(ax + b) + c with these characteristics: 0 < a < 1, b = π, c = -1.
42. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 40. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = csc(ax + b) + c with these characteristics: -1 < a < 0, b = π, c = -1.
43. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 41. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = csc(ax + b) + c with these characteristics: a = 1, b = π/2, c = -1.
44. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 42. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = csc(ax + b) + c with these characteristics: a > 1, b = π/2, c = -1.
45. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 43. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = csc(ax + b) + c with these characteristics: a < -1, b = π/2, c = -1.
46. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 44. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = csc(ax + b) + c with these characteristics: 0 < a < 1, b = π/2, c = -1.
47. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 45. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = csc(ax + b) + c with these characteristics: -1 < a < 0, b = π/2, c = -1.
48. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 46. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = a * csc(bx + c) + d with these characteristics: b = 1, c = 0, d = -1, a > 1.
49. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 47. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = a * csc(bx + c) + d with these characteristics: b > 1, c = 0, d = -1, a > 1.
50. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 48. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = a * csc(bx + c) + d with these characteristics: b < -1, c = 0, d = -1, a > 1.
51. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 49. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = a * csc(bx + c) + d with these characteristics: 0 < b < 1, c = 0, d = -1, a > 1.
52. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 50. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = a * csc(bx + c) + d with these characteristics: -1 < b < 0, c = 0, d = -1, a > 1.
53. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 51. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = a * csc(bx + c) + d with these characteristics: b = 1, c = π, d= -1, a > 1.
54. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 52. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = a * csc(bx + c) + d with these characteristics: b > 1, c = π, d = -1, a > 1.
55. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 53. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = a * csc(bx + c) + d with these characteristics: b < -1, c = π, d = -1, a > 1.
56. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 54. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = a * csc(bx + c) + d with these characteristics: 0 < b < 1, c = π, d = -1, a > 1.
57. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 55. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = a * csc(bx + c) + d with these characteristics: -1 < b < 0, c = π, d = -1, a > 1.
58. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 56. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = a * csc(bx + c) + d with these characteristics: b = 1, c = 0, d = -1, a < -1.
59. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 57. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = a * csc(bx + c) + d with these characteristics: b > 1, c = 0, d = -1, a < -1.
60. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 58. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = a * csc(bx + c) + d with these characteristics: b < -1, c = 0, d = -1, a < -1.
61. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 59. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = a * csc(bx + c) + d with these characteristics: 0 < b < 1, c = 0, d = -1, a < -1.
62. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 60. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = a * csc(bx + c) + d with these characteristics: -1 < b < 0, c = 0, d = -1, a <
-1.
63. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 61. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = a * csc(bx + c) + d with these characteristics: b = 1, c = π, d = -1, a < -1.
64. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 62. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = a * csc(bx + c) + d with these characteristics: b > 1, c = π, d = -1, a < -1.
65. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 63. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = a * csc(bx + c) + d with these characteristics: b < -1, c = π, d = -1, e < -1.
66. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 64. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = a * csc(bx + c) + d with these characteristics: 0 < b < 1, c = π, d = -1, a < -1.
67. Tutorial--Cosecant Functions in Tabular and Graph Form: Example 65. In this
tutorial, construct a function table and graph for a cosecant function of the form
y = a * csc(bx + c) + d with these characteristics: -1 < b < 0, c = π, d = -1, a <
-1.