Section 5.5 Graphs of Trigonometric Functions
In this section, we consider horizontal shifting and vertical stretching of functions. Recall the
following:
If g (x) = f (x s), then the graph of g is the graph of f shifted horizontally to x = s
If h(x) =
Section 7.3 The Law of Cosines
In this section, we introduce the Law of Cosines, and we use the Law of Cosines to solve triangles
that could not be solved with the Law of Sines in the previous section.
If a, b, c are the sides of any triangle and , , are
Section 10.3 Matrices
Matrices have many uses, most of which will be discussed in later sections. In this section, we will
use matrices to help us solve systems of linear equations. A matrix is simply a rectangular array
of numbers. Several notations are
Section 10.4 Determinants
Determinants are important mathematical tools that can frequently be used to analyze and solve
linear systems. There are various methods for nding determinants. Some of the simpler methods
only apply to 2x2 and 3x3 matrices.
Dete
Students Name:
REVIEW SECTIONS 10.1 10.2
Show all work to get full credit.
Question 1: (1 point)
[10.1.1PT]Select the type of solution for the following system .
3x+9y=v~3 §X+3 3 O 40 = O
a a K -
{m2x~6ym2 _x _3§=| v A ll
C No solution 0 = O
[3 A unique s
REVIEW SECTIONS 10.3 10.5 and 11.1 11.2 (Due Sat night, 11/25)
Consider this as the Pre-test for Test 3. Work on the questions carefully,
then send email to me (nguyen@scs.fsu.edu) with your chosen answer of
each question.
The format of the email should b
Students Name:
MAC1140-24 Review Set for Final Exam: Test 1 Material (Part 2)
Question 1: (1 point) 05 > 0: 6; c: 8
[3.1.2aPT1The graph of the quadratic function x) 2 9:2 + + 8 has
[I vertex at (35,3) Verid? X _ _\D_ - _ .9. 2 -3)
E: vertex at (1,-3) 23
Section 10.2 Linear Systems in Three Variables
This section contains material on solving systems of linear equations in three variables. Recall that
a linear equation in three variables is an equation of the form Ax + By + Cz = D, where A, B , C
and D are
Section 10.1 Systems of Linear Equations in Two Variables
This section contains material on solving systems of linear equations in two variables. Recall that a
linear equation in two variables is an equation of the form Ax + By = C , where A, B , and C ar
Section 9.4 The Hyperbola
Recall that a hyperbola can be obtained as the graph of the quadratic equation Ax2 + Bxy +
Cy + Dx + Ey + F = 0 with discriminant B 2 4AC > 0. An alternate method for obtaining a
hyperbola is given by the following denition.
2
De
Section 7.4 The Area of a Triangle
The area of a triangle is given by the following.
A = 1 bh where b is the length of base and h is the length of the altitude.
2
A = 1 ab sin
(h = a sin )
2
Example. Find the area of the triangle having a = 3, b = 4 an
Section 7.5 Simple Harmonic Motion
In this section, we dene Simple Harmonic motion, and we give some practical applications of SHM.
One should note that SHM is vibratory-type motion along a straight line. A typical example of SHM
is exhibited by a vertica
Section 8.1 Polar Coordinates
As well as rectangular cartesian coordinates, polar coordinates can also be used to locate points in
two-dimensional space. It turns out that some equations and graphs are best expressed in polar
coordinates and some in carte
Section 8.2 Equations and Graphs
In this section, we cover the standard polar graphs. Most of these graphs have simple polar equations,
but the graphs would be dicult to dene in cartesian coordinates.
Note: As with cartesian equations, when one plots a po
Section 8.3 The complex Plane
There are many practical applications of mathematics that require solutions of polynomial equations.
Solutions to all polynomial equations would not be possible, if the values of the solutions were
restricted to real numbers.
Section 8.4 Vectors
In this section, we study vectors. Vectors are very useful mathematical tools, and they are especially
important for the study of physical applications of mathematics.
A vector, denoted in these notes in boldface, like v, is a quantity
Section 8.5 The Dot Product
The dot product of two vectors is a scalar (number) that is useful in several applications. In
particular, the dot product provides an easy means for determining whether or not two vectors are
parallel or perpendicular, and for
Section 9.1 Conics
Conics and conic sections are the names ordinarily applied to the class of plots that include
parabolas, ellipses, and hyperbolas.
Conics can be obtained in the following equivalent ways:
(1) The set of points obtained by intersecting a
Section 9.2 The Parabola
Recall that a parabola can be obtained as the graph of the quadratic equation Ax2 + Bxy +
Cy + Dx + Ey + F = 0 with discriminant B 2 4AC = 0. An alternate method for obtaining a
parabola is given by the following denition.
2
Denit
Section 9.3 The Ellipse
Recall that an ellipse can be obtained as the graph of the quadratic equation Ax2 + Bxy +
Cy + Dx + Ey + F = 0 with discriminant B 2 4AC < 0. An alternate method for obtaining an
ellipse is given by the following denition.
2
Let F1
Things to know about the Test
Instructor: Ms. Hoa Nguyen (nguyen@scs.fsu.edu), MAC1140-24
Test 1:
Date: Wednesday (September 27, 2006)
Time: 1:25 pm - 2:15 pm
Location: same location as the lectures place.
The test is made by the department, not by m