College Algebra and Trigonometry

About our authors J.S. Ratti has been teaching mathematics at all levels for over 35 years. He is currently a full professor and past chair of mathematics at the University of South Florida. Professor Ratti is the author of numerous research papers in analysis, graph theory and probability. He has received several awards (including a USF Research Council Grant, USF Teaching Incentive Program/TIP Award, USF Outstanding Undergraduate Teaching Award, and Academy of Applied Sciences grants), and is the coauthor of a successful finite mathematics textbook. He enjoys both college and professional football as well as traveling. Marcus McWaters is currently an Associate Professor at the University of South Florida (USF). He is a former Chair of the Department of Mathematics and Statistics at USF. Since receiving his PhD in mathematics from the University of Florida, he has taught all levels of undergraduate and graduate courses, with class sizes ranging from 3 to 250. As Chair, he successfully structured a course delivery system for lower-level courses that improved the low retention rate in those courses at USF. He is also a founding member of the USF Center for Digital and Computational Video. When not involved with mathematics or administrative activity he enjoys traveling with his wife and two daughters, theater, waterskiing and racquetball. Leslaw Skrzypek is currently the Chair of the Department of Mathematics and Statistics at the University of South Florida. His research is in the area of Banach Spaces and Approximation Theory. He is the recipient of a Fulbright Award and a NATO Advanced Grant research award, and is a founding director of the USF Center for Complex Data Systems. Throughout his career Professor Skrzypek has enjoyed teaching all levels of courses, from remedial to graduate real analysis. Over the years he also has been involved in training students for the Mathematical Olympiads. He enjoys nature, listening to music and spending time with his family.

Table of Contents



BASIC CONCEPTS OF ALGEBRA

P.1 The Real Numbers and Their Properties
P.2 Integer Exponents and Scientific Notation
P.3 Polynomials
P.4 Factoring Polynomials
P.5 Rational Expressions
P.6 Rational Exponents and Radicals
Chapter P Review and Tests
Review Exercises
Practice Test


EQUATIONS AND INEQUALITIES

1.1 Linear Equations in One Variable
1.2 Applications of Linear Equations: Modeling
1.3 Quadratic Equations
1.4 Complex Numbers: Quadratic Equations with Complex Solutions
1.5 Solving Other Types of Equations
1.6 Inequalities
1.7 Equations and Inequalities Involving Absolute Value
Chapter 1 Review and Tests
Review Exercises
Practice Test A
Practice Test B


GRAPHS AND FUNCTIONS

2.1 The Coordinate Plane
2.2 Graphs of Equations
2.3 Lines
2.4 Functions
2.5 Properties of Functions
2.6 A Library of Functions
2.7 Transformations of Functions
2.8 Combining Functions; Composite Functions
2.9 Inverse Functions
Chapter 2 Review and Tests
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P—2


POLYNOMIAL AND RATIONAL FUNCTIONS

3.1 Quadratic Functions
3.2 Polynomial Functions
3.3 Dividing Polynomials
3.4 The Real Zeros of a Polynomial Function
3.5 The Complex Zeros of a Polynomial Function
3.6 Rational Functions
3.7 Variation
Chapter 3 Review and Tests
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P—3


EXPONENTIAL AND LOGARITHMIC FUNCTIONS

4.1 Exponential Functions
4.2 Logarithmic Functions
4.3 Rules of Logarithms
4.4 Exponential and Logarithmic Equations and Inequalities
4.5 Logarithmic Scales; Modeling
Chapter 4 Review and Tests
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P—4


TRIGONOMETRIC FUNCTIONS

5.1 Angles and Their Measure
5.2 Right-Triangle Trigonometry
5.3 Trigonometric Functions of Any Angle; The Unit Circle
5.4 Graphs of the Sine and Cosine Functions
5.5 Graphs of the Other Trigonometric Functions
5.6 Inverse Trigonometric Functions
Chapter 5 Review and Tests
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P—5


TRIGONOMETRIC IDENTITIES AND EQUATIONS

6.1 Trigonometric Identities
6.2 Sum and Difference Formulas
6.3 Double-Angle and Half-Angle Formulas
6.4 Product-to-Sum and Sum-to-Product Formulas
6.5 Trigonometric Equations I
6.6 Trigonometric Equations II
Chapter 6 Review and Tests
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P—6


APPLICATIONS OF TRIGONOMETRIC FUNCTIONS

7.1 The Law of Sines
7.2 The Law of Cosines
7.3 Areas of Polygons Using Trigonometry
7.4 Vectors
7.5 The Dot Product
7.6 Polar Coordinates
7.7 Polar Form of Complex Numbers; DeMoivre’s Theorem
Chapter 7 Review and Tests
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P—7


SYSTEMS OF EQUATIONS AND INEQUALITIES

8.1 Systems of Linear Equations in Two Variables
8.2 Systems of Linear Equations in Three Variables
8.3 Partial-Fraction Decomposition
8.4 Systems of Nonlinear Equations
8.5 Systems of Inequalities
8.6 Linear Programming
Chapter 8 Review and Tests
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P—8


MATRICES AND DETERMINANTS

9.1 Matrices and Systems of Equations
9.2 Matrix Algebra
9.3 The Matrix Inverse
9.4 Determinants and Cramer’s Rule
Chapter 9 Review and Tests
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P—9


CONIC SECTIONS

10.1 Conic Sections: Overview
10.2 The Parabola
10.3 The Ellipse
10.4 The Hyperbola
Chapter 10 Review and Tests
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P—10


FURTHER TOPICS IN ALGEBRA

11.1 Sequences and Series
11.2 Arithmetic Sequences; Partial Sums
11.3 Geometric Sequences and Series
11.4 Mathematical Induction
11.5 The Binomial Theorem
11.6 Counting Principles
11.7 Probability
Chapter 11 Review and Tests
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P—11



Answers to Selected Exercises Credits Index