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 PropertiesP.2 Integer Exponents and Scientific NotationP.3 PolynomialsP.4 Factoring PolynomialsP.5 Rational ExpressionsP.6 Rational Exponents and RadicalsChapter P Review and TestsReview ExercisesPractice TestEQUATIONS AND INEQUALITIES 1.1 Linear Equations in One Variable1.2 Applications of Linear Equations: Modeling1.3 Quadratic Equations1.4 Complex Numbers: Quadratic Equations with Complex Solutions1.5 Solving Other Types of Equations1.6 Inequalities1.7 Equations and Inequalities Involving Absolute ValueChapter 1 Review and TestsReview ExercisesPractice Test APractice Test BGRAPHS AND FUNCTIONS 2.1 The Coordinate Plane2.2 Graphs of Equations2.3 Lines2.4 Functions2.5 Properties of Functions2.6 A Library of Functions2.7 Transformations of Functions2.8 Combining Functions; Composite Functions2.9 Inverse FunctionsChapter 2 Review and TestsReview ExercisesPractice Test APractice Test BCumulative Review Exercises Chapters P—2POLYNOMIAL AND RATIONAL FUNCTIONS 3.1 Quadratic Functions3.2 Polynomial Functions3.3 Dividing Polynomials3.4 The Real Zeros of a Polynomial Function3.5 The Complex Zeros of a Polynomial Function3.6 Rational Functions3.7 VariationChapter 3 Review and TestsReview ExercisesPractice Test APractice Test BCumulative Review Exercises Chapters P—3EXPONENTIAL AND LOGARITHMIC FUNCTIONS 4.1 Exponential Functions4.2 Logarithmic Functions4.3 Rules of Logarithms4.4 Exponential and Logarithmic Equations and Inequalities4.5 Logarithmic Scales; ModelingChapter 4 Review and TestsReview ExercisesPractice Test APractice Test BCumulative Review Exercises Chapters P—4TRIGONOMETRIC FUNCTIONS 5.1 Angles and Their Measure5.2 Right-Triangle Trigonometry5.3 Trigonometric Functions of Any Angle; The Unit Circle5.4 Graphs of the Sine and Cosine Functions5.5 Graphs of the Other Trigonometric Functions5.6 Inverse Trigonometric FunctionsChapter 5 Review and TestsReview ExercisesPractice Test APractice Test BCumulative Review Exercises Chapters P—5TRIGONOMETRIC IDENTITIES AND EQUATIONS 6.1 Trigonometric Identities6.2 Sum and Difference Formulas6.3 Double-Angle and Half-Angle Formulas6.4 Product-to-Sum and Sum-to-Product Formulas6.5 Trigonometric Equations I6.6 Trigonometric Equations IIChapter 6 Review and TestsReview ExercisesPractice Test APractice Test BCumulative Review Exercises Chapters P—6APPLICATIONS OF TRIGONOMETRIC FUNCTIONS 7.1 The Law of Sines7.2 The Law of Cosines7.3 Areas of Polygons Using Trigonometry7.4 Vectors7.5 The Dot Product7.6 Polar Coordinates7.7 Polar Form of Complex Numbers; DeMoivre’s TheoremChapter 7 Review and TestsReview ExercisesPractice Test APractice Test BCumulative Review Exercises Chapters P—7SYSTEMS OF EQUATIONS AND INEQUALITIES 8.1 Systems of Linear Equations in Two Variables8.2 Systems of Linear Equations in Three Variables8.3 Partial-Fraction Decomposition8.4 Systems of Nonlinear Equations8.5 Systems of Inequalities8.6 Linear ProgrammingChapter 8 Review and TestsReview ExercisesPractice Test APractice Test BCumulative Review Exercises Chapters P—8MATRICES AND DETERMINANTS 9.1 Matrices and Systems of Equations9.2 Matrix Algebra9.3 The Matrix Inverse9.4 Determinants and Cramer’s RuleChapter 9 Review and TestsReview ExercisesPractice Test APractice Test BCumulative Review Exercises Chapters P—9CONIC SECTIONS 10.1 Conic Sections: Overview10.2 The Parabola10.3 The Ellipse10.4 The HyperbolaChapter 10 Review and TestsReview ExercisesPractice Test APractice Test BCumulative Review Exercises Chapters P—10FURTHER TOPICS IN ALGEBRA 11.1 Sequences and Series11.2 Arithmetic Sequences; Partial Sums11.3 Geometric Sequences and Series11.4 Mathematical Induction11.5 The Binomial Theorem11.6 Counting Principles11.7 ProbabilityChapter 11 Review and TestsReview ExercisesPractice Test APractice Test BCumulative Review Exercises Chapters P—11Answers to Selected Exercises Credits Index