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College Algebra and Trigonometry, 4th edition

Published by Pearson (January 3, 2018) © 2019

  • J S Ratti University of South Florida
  • Marcus S. McWaters University of South Florida
  • Leslaw Skrzypek University Of South Florida

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For courses in Algebra & Trigonometry.

Effectively emphasizes concept development and real-life applications

The Ratti/McWaters/Skrzypek series draws from the authors' extensive classroom experience to connect conceptual understanding while maintaining course rigor. Just-in-time review throughout College Algebra and Trigonometry, 4th Edition ensures that all students are brought to the same level before being introduced to new concepts. Numerous applications motivate students to apply the concepts and skills they learn in college algebra to other courses, including the physical and biological sciences, engineering, economics, and to on-the-job and everyday problem solving.

Hallmark features of this title

  • Section opener with application: Section Objectives are stated and numbered, then referenced again in the margins. An Application follows with a motivating anecdote or interesting problem. Later, an example related to this Application is solved using the mathematics covered in the section.
  • Work it out approach encourages students to practice the material frequently, with ample opportunities to master the material by solving problems and applying their understanding.
    • Procedure in Action introduces steps in the context of a worked-out example.
    • Examples include a wide range of computational, conceptual and modern applied problems.
    • All examples are followed by a Practice Problem.
  • Definitions, Theorems, Properties and Rules are all boxed and titled clearly.

New and updated features of this title

  • Over 20% of exercises are updated, with over 500 brand-new exercises added.  New exercises feature applications that connect with students' everyday experiences and enhance their conceptual understanding of graphing.
    • A revised balance of exercises provides a smoother transition from less-challenging to more-challenging exercises. Well-crafted Exercises are offered in a quantity, quality and variety that meets the needs of all students.
  • New Concepts and Vocabulary exercises begin each exercise set with problems that assess the student's grasp of the definitions and ideas introduced in that section. These true/false and fill-in-the-blank exercises help to rapidly identify comprehension gaps.
  • New Graph and Data-Related Exercises show how to extract information about real-world situations from a graphical representation of that situation, and how to recover algebraic or trigonometric formulations of a graph by using key characteristics of that graph.
  • New Getting Ready for the Next Section exercises end each exercise set with problems that provide a review of concepts and skills to be used in the following section.
  • New Modeling Exercises: A section on building linear, exponential, logarithmic and power models from data in Chapter 4 contains new exercises using each type of model.

Features of MyLab Math for the 4th Edition

  • New Concept and Vocabulary exercises assess the student's grasp of the definitions and ideas introduced in that section; assignable in MyLab Math and Learning Catalytics.
  • Assignable Video Assessment questions are tied to Example Solutions videos, designed to check students' understanding of the important math concepts covered in the video.  
  • The new Video Notebook guide gives students a structured place to take notes and work on the example problems as they watch the Example Solution videos. Definitions, examples and important concepts are highlighted, and helpful hints are pointed out along the way.  
  • New Set Up & Solve exercises require students to show the setup of the solution for a particular exercise as well as the solution, helping them develop an overall problem-solving strategy before attempting the solution.
  • New exercises prepare students for material in the next section. Each exercise section ends with a set of exercises that provide a review of concepts and skills that will be used in the following section.
  • New Enhanced Sample Assignments make course set-up easier by giving instructors a starting point for each section. Each assignment, handpicked by the authors to align with this text, includes a thoughtful mix of question types specific to that topic.

P. 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

1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

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.

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