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Precalculus: A Right Triangle Approach, 4th edition

Published by Pearson (January 8, 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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Hallmark features of this title

  • Section opener with application: Each section opens with a list of prerequisite topics which students can review.
    • The section Objectives are clearly stated and numbered, then referenced again in the margin of the lesson where the objective's topic is taught.
    • An Application follows with a motivating anecdote or an interesting problem. An example later in the section relating to this application and identified by the same icon is then solved using the mathematics covered in the section.
  • Work it out: Students are encouraged to practice the material frequently, with ample opportunities to master the material by solving problems and applying understanding.
    • Procedure in Action introduces procedure steps within the context of a worked-out example. Important multistep procedures are presented in a 2-column format.
    • Examples include a wide range of computational, conceptual and modern applied problems carefully selected to build confidence, competency and understanding. Every example has a title indicating its purpose and presents a detailed solution containing annotated steps. A Practice Problem follows every example for students to check their understanding.

New and updated features of this title

  • Over 20% of exercises are updated, and a substantial amount of brand-new exercises have been added.
    • An improved balance of exercises provides a smoother transition from the less-challenging to the more-challenging exercises. Exercises are clearly labeled for instructors' and students' understanding of exercise expectations.
    • Getting Ready for the Next Section exercises end each exercise set with problems that provide a review of concepts and skills that will be used in the following section.
  • Graph and Data-Related exercises throughout the text demonstrate how to extract information about real-world situations from a graphical representation of that situation, as well as how to recover algebraic or trigonometric formulations of a graph by using key characteristics of that graph.
  • Modeling Exercises: A section on building linear, exponential, logarithmic, and power models from data is added in Chapter 4, containing new exercises using each type of model.
  • 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 gaps in comprehension of the material in that section.

Features of MyLab Math for the 4th Edition

  • Skill Builder offers adaptive practice that is designed to increase students' ability to complete their assignments. By monitoring student performance on their homework, Skill Builder adapts to each student's needs and provides just-in-time, in-assignment practice to help them improve their proficiency of key learning objectives.
  • Enhanced Sample Assignments make course set-up easier by giving instructors a starting point for each chapter. Each assignment, handpicked by the authors, includes a thoughtful mix of question types (e.g., conceptual, skills, etc.) specific to that topic.
  • MyLab Math Question Types enable students to develop and gauge their conceptual understanding.
  • Concept and Vocabulary exercises start each section by assessing 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 gaps in comprehension of the material in that section and are assignable in MyLab Math and Learning Catalytics.
  • Video Assessment questions are assignable MyLab Math exercises tied to Example Solutions videos. The questions are designed to check students' understanding of the important math concepts covered in the video. The videos and Video Assessment questions provide an active learning environment where students can work at their own pace.
  • The Video Notebook is a guide that 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. The notebook is available in MyLab Math for download.

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 2 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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