Precalculus A Right Triangle Approach

The Ratti/McWaters/Skrzypek series draws from the authors’ extensive classroom experience to connect concepts while maintaining course rigor. Just-in-time review throughout Precalculus: A Right Triangle Approach, 4th Edition ensures that all students are brought to the same level before being introduced to new concepts. Numerous applications are used to help students apply the concepts and skills they learn in college algebra and trigonometry to other courses (including the physical and biological sciences, engineering, economics, and to on-the-job and everyday problem solving).

Students are given ample opportunities to think about important mathematical ideas and to practice and apply algebraic skills. Because mathematical concepts are developed thoroughly and with clearly defined terminology, students see the “why” behind those concepts—paving the way for a deeper understanding, better retention, less reliance on rote memorization, and ultimately more success.

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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, water¿skiing, 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.

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

1.1 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

2.1 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

3.1 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

4.1 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

5.1 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  

6.1 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

7.1 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 745

7.6 Polar Coordinates 756

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

8.1 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

9.1 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

10.1 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

11.1 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

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