# Precalculus: A Unit Circle Approach, 4th edition

Published by Pearson (July 3, 2022) © 2023

**J S Ratti**University of South Florida**Marcus S. McWaters**University of South Florida**Leslaw Skrzypek**University Of South Florida**Jessica Bernards**Portland Community College**Wendy Fresh**Portland Community College

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## MyLab

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For courses in Precalculus.

### Solid preparation for calculus with an engaging, friendly approach

**Precalculus: A Unit Circle Approach** draws from the authors' extensive classroom experience to build conceptual understanding and skills so that students are ready for calculus. In the **4th Edition**, new resources help students reach their full potential, including author-created instructional videos, note-taking guides, and study skills resources, plus built-in support for corequisite courses. Nationally recognized instructors Jessica Bernards and Wendy Fresh join the author team in this revision, helping students master challenging concepts by making them as accessible as possible.

### Hallmark features of this title

**Relevant applications**motivate the content of each chapter and each section. Within sections, the opening application appears in a related example and in the exercise set.**Integrated study aids**help make challenging math more accessible. For example,**Procedure in Action**shows procedural steps within the context of a worked-out example.**Warnings**alert students to common errors and pitfalls.**Key Ideas at a Glance**is a one-page visual study guide at the end of each chapter.**Exercise sets**are varied and comprehensive, consisting of the following sections: (a) Concepts and Vocabulary, (b) Building Skills, (c) Applying the Concepts, and (d) Beyond the Basics (more theoretical exercises, ideal for honors students or extra credit).**Getting Ready for the Next Section**exercises provide a just-in-time diagnostic of prerequisite skills.

### New and updated features of this title

**Getting Ready for the Next Section**lists Review Concepts and Review Skills for students to brush up on before starting new material.**Key Ideas At a Glance**highlights key concepts on a single page in a unique visual way for each chapter right before the chapter review and tests. Accompanying exercises help students test their understanding.**Improved balance of exercises**provides a smooth transition from less challenging to more challenging.**Section-opening applications now extend to exercises.**Every section opens with discussion of an application that relates to the topics introduced in that section. While examples are paired with each application, the 4th Edition also includes problems in the exercise set tied to that application, so students can apply the math to a real-world problem.**Active Learning Exercises**end many sections. These are accompanied by an Interactive Figure powered by GeoGebra, which is accessed directly within the eText or a short URL, or by scanning a QR code in the print text. Students manipulate the figure to explore the math and use the figure to answer the exercises.

### Features of MyLab Math for the 4th Edition

**Nationally recognized instructors Jessica Bernards and Wendy Fresh**join the author team in this revision, helping students master challenging concepts by making them as accessible as possible.**Updated video program**shows Bernards and Fresh breaking down complex topics using their extensive teaching experience and the text's proven study features like Procedure in Action and Warnings. The**revised student Video Notebook**helps students take notes and work example problems as they watch.**New Mathematical Study Skills videos**motivate students to stick with the course and offer tips.**Corequisite Support Content**includes instructional videos and assignable algorithmic exercises, worksheets for each objective and classroom activities.- Editable
**Pre-built Assignments:****Learning Assignments**include short objective videos and exercises to check understanding, especially helpful for online or flipped classes.**Enhanced****Assignments**are geared to maximize students' performance.**Integrated Review**helps students who need a refresher and personalizes to their individual needs. - Assignable
**Interactive Figures**explore concepts through directed exploration and manipulation. **GeoGebra Exercises**are gradable graphing and computational exercises that help students demonstrate their understanding.

### Features of Pearson eText for the 4th Edition

**Objective, section and select exercises**have new videos in MyLab Math.**Active learning exercise links**are available.

### 1. Graphs and Functions

- 1.1 The Coordinate Plane
- 1.2 Graphs of Equations
- 1.3 Lines
- 1.4 Functions
- 1.5 Properties of Functions
- 1.6 A Library of Functions
- 1.7 Transformations of Functions
- 1.8 Combining Functions; Composite Functions
- 1.9 Inverse Functions
- Key Ideas At a Glance
- Review Exercises
- Practice Test

### 2. Polynomial and Rational Functions

- 2.1 Quadratic Functions
- 2.2 Polynomial Functions
- 2.3 Dividing Polynomials and the Rational Zeros Test
- 2.4 Rational Functions
- 2.5 Polynomial and Rational Inequalities
- 2.6 Zeros of a Polynomial Function
- 2.7 Variation
- Key Ideas At a Glance
- Review Exercises
- Practice Test
- Cumulative Review Exercises Chapters 1-2

### 3. Exponential and Logarithmic Functions

- 3.1 Exponential Functions
- 3.2 Logarithmic Functions
- 3.3 Rules of Logarithms
- 3.4 Exponential and Logarithmic Equations and Inequalities
- 3.5 Logarithmic Scales; Modeling
- Key Ideas At a Glance
- Review Exercises
- Practice Test
- Cumulative Review Exercises Chapters 1-3

### 4. Trigonometric Functions

- 4.1 Angles and Their Measure
- 4.2 The Unit Circle; Trigonometric Functions of Real Numbers
- 4.3 Trigonometric Functions of Angles
- 4.4 Graphs of the Sine and Cosine Functions
- 4.5 Graphs of the Other Trigonometric Functions
- 4.6 Inverse Trigonometric Functions
- Key Ideas At a Glance
- Review Exercises
- Practice Test
- Cumulative Review Exercises Chapters 1-4

### 5. Analytic Trigonometry

- 5.1 Trigonometric Identities
- 5.2 Sum and Difference Formulas
- 5.3 Double-Angle and Half-Angle Formulas
- 5.4 Product-to-Sum and Sum-to-Product Formulas
- 5.5 Trigonometric Equations I
- 5.6 Trigonometric Equations II
- Key Ideas At a Glance
- Review Exercises
- Practice Test
- Cumulative Review Exercises Chapters 1-5

### 6. Applications of Trigonometric Functions

- 6.1 Right-Triangle Trigonometry
- 6.2 The Law of Sines
- 6.3 The Law of Cosines
- 6.4 Vectors
- 6.5 The Dot Product
- 6.6 Polar Coordinates
- 6.7 Polar Form of Complex Numbers; DeMoivre's Theorem
- Key Ideas At a Glance
- Review Exercises
- Practice Test
- Cumulative Review Exercises Chapters 1-6

### 7. Systems of Equations and Inequalities

- 7.1 Systems of Equations in Two Variables
- 7.2 Systems of Linear Equations in Three Variables
- 7.3 Systems of Inequalities
- 7.4 Matrices and Systems of Equations
- 7.5 Determinants and Cramer's Rule
- 7.6 Partial-Fraction Decomposition
- 7.7 Matrix Algebra
- 7.8 The Matrix Inverse
- Key Ideas At a Glance
- Review Exercises
- Practice Test
- Cumulative Review Exercises Chapters 1-7

### 8. Analytic Geometry

- 8.1 Conic Sections: Overview
- 8.2 The Parabola
- 8.3 The Ellipse
- 8.4 The Hyperbola
- 8.5 Rotation of Axes
- 8.6 Polar Equations of Conics
- 8.7 Parametric Equations
- Key Ideas At a Glance
- Review Exercises
- Practice Test
- Cumulative Review Exercises Chapters 1-8

### 9. Further Topics in Algebra

- 9.1 Sequences and Series
- 9.2 Arithmetic Sequences; Partial Sums
- 9.3 Geometric Sequences and Series
- 9.4 Mathematical Induction
- 9.5 The Binomial Theorem
- 9.6 Counting Principles
- 9.7 Probability
- Key Ideas At a Glance
- Review Exercises
- Practice Test
- Cumulative Review Exercises Chapters 1-9

### 10. An Introduction to Calculus

- 10.1 Finding Limits Using Tables and Graphs
- 10.2 Finding Limits Algebraically
- 10.3 Infinite Limits and Limits at Infinity
- 10.4 Introduction to Derivatives
- 10.5 Area and the Integral
- Key Ideas At a Glance
- Review Exercises
- Practice Test

### A. Review

- A.1 The Real Numbers; Integer Exponents
- A.2 Polynomials
- A.3 Rational Expressions
- A.4 Radicals and Rational Exponents
- A.5 Topics in Geometry
- A.6 Equations
- A.7 Inequalities
- A.8 Complex Numbers

##### Answers to Selected Exercises

##### Credits

##### Index

### About our authors

**J.S. Ratti** (1935 - 2018) taught mathematics at all levels for over 35 years, most recently as a full professor and past chair of mathematics at the University of South Florida. Professor Ratti was the author of numerous research papers in analysis, graph theory and probability. He 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; he was the coauthor of a successful finite mathematics textbook.

**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.

**Jessica Bernards** has been teaching mathematics since 2005. She began her career at the high-school level and transitioned to teaching at Portland Community College in 2010. She has taught a wide range of mathematics courses from developmental math up to calculus and has created curricula for each level. Bernards is a member of AMATYC's Project ACCCESS Cohort 9, where she developed a math study skills program that is now used across the US. In 2017, she was the honored recipient of the Leila and Simon Peskoff AMATYC Award for her work with Project ACCCESS, and in 2021 received the AMATYC Teaching Excellence Award.

**Wendy Fresh** has been a full-time instructor at Portland Community College (PCC) since 1997. She has taught a wide range of classes, from developmental math through calculus, both on campus and online. Fresh began her teaching career in 1992 in both rural and urban high schools. Her love of creating curricula to bring classrooms to life has led to work with technologies that complement her many courses. She earned her bachelor's degree in mathematics education from the University of Oregon and her master's degree in the teaching of mathematics from Portland State University.

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