Algebra and Trigonometry: A Graphing Approach, 1/e
Dale Varberg, Hamline University
Thomas D. Varberg, Mccalester College
Published October, 1995 by Prentice Hall Engineering/Science/Mathematics
Copyright 1996, 579 pp.
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Algebra/Trig with Graphing Calculators-Mathematics
This second in a series of three texts covers the traditional topics for
Algebra and Trigonometry with a unique emphasis on concepts that are valuable
to other courses or other applications, especially those that can be explored
and illustrated on a graphics calculator. It de-emphasizes the more
manipulative skills in favor of visualization, graphing, data analysis, and
modeling of problems from the physical world.
makes mathematics come alive, using the graphics calculator to study
functions in-depth, including...
constructs a problem-solving framework composed of...
- finding their zeros.
- discovering where they increase and decrease.
- identifying their maxima and minima.
- analyzing their asymptotic behavior.
- calculating their rates of change.
- viewing the graphs of several functions at once.
- finding their points of intersection.
- discovering where one is larger than another.
- visualizing motion by watching graphs generated in real-time
through parametric representation.
provides special labels for difficult (Challenge)
or skill- developing/experimentation (P-Projects) problems
- Teaserssection-opening problems that entice
students to seek solutions.
- section-ending problem sets divided into two partsPart
A (Skills and Techniques) offers simpler problem pairs which
follow the text and its examples closely; and Part B (Applications
and Extensions)includes a variety of more demanding problems
that make use of the skills learned in Part A in the broad context
of mathematical, scientific and business applications.
offers many options for instructors to custom-tailor the
text's organization to suit their particular course objectives.
introduces programming of graphics calculators in the last
chapter where it fits naturally with sequences and series.
1. Numbers, Calculations and Basic Algebra.
The Integers and the Rational Numbers. Real Numbers and
their Properties. Order and Averages. Exponents and their Properties.
Polynomials and their Factors. Rational Expressions. The Complex Numbers.
2. Equations and Inequalities.
Solving Equations Algebraically. Equations and Applications.
Displaying Equations Geometrically. Graphs with Graphics Calculators.
Inequalities and Absolute Values. Lines. Some Important Quadratic
Curves. Linear Regression.
3. Functions and Their Graphs.
The Function Concept. Linear Functions. Quadratic Functions.
More on Graphics Calculators. Polynomial Functions. Rational Functions.
Combinations of Functions. Inverse Functions. Special Functions.
4. Exponential and Logarithmic Functions.
Exponential Functions. Logarithms and Logarithmic Functions.
Scientific Applications. Business Applications. Nonlinear Regression.
5. The Trigonometric Functions.
Right Triangle Trigonometry. General Angles and Arcs. The
Sine and Cosine Functions. Graphs of the Sine and Cosine Functions.
Four More Trigonometric Functions. Inverse Trigonometric Functions.
6. Trigonometric Identities, Equations and Laws.
Basic Trigonometric Identities. Addition Identities. More
Identities. Trigonometric Equations. The Law of Sines. The Law of
7. Systems of Equations and Inequalities.
Equivalent Systems of Equations. Solving Systems Using Matrices.
The Algebra of Matrices. Inverses of Matrices. Determinants. Systems
8. Analytic Geometry.
Parabolas. Ellipses. Hyperbolas. Rotations. Parametric Equations.
Polar Coordinates. Polar Equations of Conics.
9. Sequences, Counting and Probability.
Arithmetic Sequences and Sums. Geometric Sequences and Sums.
General Sequences and Programming. Mathematical Induction. The Binomial
Formula. Counting Ordered Arrangements. Counting Unordered Collections.
Introduction to Probablility. Independence in Probability Problems.
Answers to Selected Problems.