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## About *Algebra and Trigonometry 2e*

*Algebra and Trigonometry 2e* provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensures that the book meets the needs of a variety of courses. *Algebra and Trigonometry 2e* offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.

### Coverage and Scope

In determining the concepts, skills, and topics to cover, we engaged dozens of highly experienced instructors with a range of student audiences. The resulting scope and sequence proceeds logically while allowing for a significant amount of flexibility in instruction.

Chapters 1 and 2 provide both a review and foundation for study of functions that begins in Chapter 3. The authors recognize that while some institutions may find this material a prerequisite, other institutions have told us that they have a cohort that needs the prerequisite skills built into the course.

- Chapter 1: Prerequisites
- Chapter 2: Equations and Inequalities

Chapters 3–6: The Algebraic Functions

- Chapter 3: Functions
- Chapter 4: Linear Functions
- Chapter 5: Polynomial and Rational Functions
- Chapter 6: Exponential and Logarithm Functions

Chapters 7–10: A Study of Trigonometry

- Chapter 7: The Unit Circle: Sine and Cosine Functions
- Chapter 8: Periodic Functions
- Chapter 9: Trigonometric Identities and Equations
- Chapter 10: Further Applications of Trigonometry

Chapters 11–13: Further Study in Algebra and Trigonometry

- Chapter 11: Systems of Equations and Inequalities
- Chapter 12: Analytic Geometry
- Chapter 13: Sequences, Probability, and Counting Theory

### Development Overview

OpenStax *Algebra and Trigonometry 2e* is the product of a collaborative effort by a group of dedicated authors, editors, and instructors whose collective passion for this project has resulted in a text that is remarkably unified in purpose and voice. Special thanks is due to our Lead Author, Jay Abramson of Arizona State University, who provided the overall vision for the book and oversaw the development of each and every chapter, drawing up the initial blueprint, reading numerous drafts, and assimilating field reviews into actionable revision plans for our authors and editors.

The collective experience of our author team allowed us to pinpoint the subtopics, exceptions, and individual connections that give students the most trouble. The textbook is therefore replete with well-designed features and highlights which help students overcome these barriers. As the students read and practice, they are coached in methods of thinking through problems and internalizing mathematical processes.

### Accuracy of the Content

We understand that precision and accuracy are imperatives in mathematics, and undertook a dedicated accuracy program led by experienced faculty.Examples, art, problems, and solutions were reviewed by dedicated faculty, with a separate team evaluating the answer key and solutions.

The text also benefits from years of usage by thousands of faculty and students. A core aspect of the second edition revision process included consolidating and ensuring consistency with regard to any errata and corrections that have been during in the series’ extensive usage and incorporation into homework systems.

### Changes to the Second Edition

The *Algebra and Trigonometry 2e* revision focused on mathematical clarity and accuracy as well as inclusivity. Examples, Exercises, and Solutions were reviewed by multiple faculty experts. All improvement suggestions and errata updates, driven by faculty and students from several thousand colleges, were considered and unified across the different formats of the text.

OpenStax and our authors are aware of the difficulties posed by shifting problem and exercise numbers when textbooks are revised. In an effort to make the transition to the 2nd edition as seamless as possible, we have minimized any shifting of exercise numbers.

The revision also focused on supporting inclusive and welcoming learning experiences. The introductory narratives, example and problem contexts, and even many of the names used for fictional people in the text were all reviewed using a diversity, equity, and inclusion framework. Several hundred resulting revisions improve the balance and relevance to the students using the text, while maintaining a variety of applications to diverse careers and academic fields. In particular, explanations of scientific and historical aspects of mathematics have been expanded to include more contributors. For example, the authors added additional historical and multicultural context regarding what is widely known as Pascal’s Triangle, and similarly added details regarding the international process of decoding the Enigma machine (including the role of Polish college students). Several chapter opening narratives and in-chapter references are completely new, and contexts across all chapters were specifically reviewed for equity in gender representation and connotation.

Finally, prior to the release of this edition, OpenStax published a series of Corequisite Skillsheets to support different models and approaches to instruction. These remain available, and are described in more detail below.

### Pedagogical Foundations and Features

#### Learning Objectives

Each chapter is divided into multiple sections (or modules), each of which is organized around a set of learning objectives. The learning objectives are listed explicitly at the beginning of each section and are the focal point of every instructional element

#### Narrative text

Narrative text is used to introduce key concepts, terms, and definitions, to provide real-world context, and to provide transitions between topics and examples. Throughout this book, we rely on a few basic conventions to highlight the most important ideas:

- Key terms are boldfaced, typically when first introduced and/or when formally defined.
- Key concepts and definitions are called out in a blue box for easy reference.

#### Examples

Each learning objective is supported by one or more worked examples, that demonstrate the problem-solving approaches that students must master. The multiple Examples model different approaches to the same type of problem, or introduce similar problems of increasing complexity.

All Examples follow a simple two- or three-part format. The question clearly lays out a mathematical problem to solve. The Solution walks through the steps, usually providing context for the approach—in other words, why the instructor is solving the problem in a specific manner. Finally, the Analysis (for select Examples) reflects on the broader implications of the Solution just shown. Examples are followed by a Try It question, as explained below.

#### Figures

*Algebra and Trigonometry 2e* contains more than 2000 figures and illustrations, the vast majority of which are graphs and diagrams. Art throughout the text adheres to a clear, understated style, drawing the eye to the most important information in each figure while minimizing visual distractions. Color contrast is employed with discretion to distinguish between the different functions or features of a graph.

#### Supporting Features

Several elements contribute to and check understanding.

- A
**“How To”**is a list of steps necessary to solve a certain type of problem. A How To typically precedes an Example that proceeds to demonstrate the steps in action. - A
**“Try It”**exercise immediately follows an Example or a set of related Examples, providing the student with an immediate opportunity to solve a similar problem. In the PDF and the Web View version of the text, answers to the Try It exercises are located in the Answer Key. - A
**Q&A**may appear at any point in the narrative, but most often follows an Example. This feature pre-empts misconceptions by posing a commonly asked yes/no question, followed by a detailed answer and explanation. - The
**“Media”**icon appears at the conclusion of each section, just prior to the Section Exercises. This icon marks a list of links to online video tutorials that reinforce the concepts and skills introduced in the section.

While we have selected tutorials that closely align to our learning objectives, we did not produce these tutorials, nor were they specifically produced or tailored to accompany *Algebra and Trigonometry 2e*.

#### Section Exercises

Each section of every chapter concludes with a well-rounded set of exercises that can be assigned as homework or used selectively for guided practice. With over 6300 exercises across the 13 chapters, instructors should have plenty from which to choose.

Section Exercises are organized by question type, and generally appear in the following order:

**Verbal**questions assess conceptual understanding of key terms and concepts.**Algebraic**problems require students to apply algebraic manipulations demonstrated in the section.**Graphical**problems assess students’ ability to interpret or produce a graph.**Numeric**problems require the student to perform calculations or computations.**Technology**problems encourage exploration through use of a graphing utility, either to visualize or verify algebraic results or to solve problems via an alternative to the methods demonstrated in the section.**Extensions**pose problems more challenging than the Examples demonstrated in the section. They require students to synthesize multiple learning objectives or apply critical thinking to solve complex problems.**Real-World Applications**present realistic problem scenarios from fields such as physics, geology, biology, finance, and the social sciences.

#### Chapter Review Features

Each chapter concludes with a review of the most important takeaways, as well as additional practice problems that students can use to prepare for exams.

**Key Terms**provides a formal definition for each bold-faced term in the chapter.**Key Equations**presents a compilation of formulas, theorems, and standard-form equations.**Key Concepts**summarizes the most important ideas introduced in each section, linking back to the relevant Example(s) in case students need to review.**Chapter Review Exercises**include 40-80 practice problems that recall the most important concepts from each section.**Practice Test**includes 25-50 problems assessing the most important learning objectives from the chapter. Note that the practice test is not organized by section, and may be more heavily weighted toward cumulative objectives as opposed to the foundational objectives covered in the opening sections.

#### Corequisite Support

Each *Algebra and Trigonometry 2e* section is paired with a thoughtfully developed, topically aligned skills module that prepares students for the course material. Sharon North (St. Louis Community College) developed a coordinated set of support resources, which provide review, instruction, and practice for algebra students. The author team identified foundational skills and concepts, then mapped them to each module. The corequisite sections include conceptual overviews, worked examples, and guided practice; they incorporate relevant material from OpenStax’s Developmental Math series. They are available as separate, openly accessible downloads from the student and instructor resources pages accompanying the text.

#### Answers to Questions in the Book

Students are provided with answers to Examples directly below the question. The answer key in the book contains all answers to Try It questions as well as answers to odd-numbered Section Exercises, Review Exercises, and Practice Tests. In order to allow instructors as much flexibility as possible, even-numbered answers to Section Exercises, Review Exercises, and Practice Tests are provided only to instructors via the Instructor Answer Guide on the Instructor Resources page.

#### Additional Resources

##### Student and Instructor Resources

We’ve compiled additional resources for both students and instructors, including Getting Started Guides, instructor solution manual, Corequisite skillsheets, and PowerPoint slides. Instructor resources require a verified instructor account, which can be requested on your openstax.org log-in. Take advantage of these resources to supplement your OpenStax book.

#### Community Hubs

OpenStax partners with the Institute for the Study of Knowledge Management in Education (ISKME) to offer Community Hubs on OER Commons—a platform for instructors to share community-created resources that support OpenStax books, free of charge. Through our Community Hubs, instructors can upload their own materials or download resources to use in their own courses, including additional ancillaries, teaching material, multimedia, and relevant course content. We encourage instructors to join the hubs for the subjects most relevant to your teaching and research as an opportunity both to enrich your courses and to engage with other faculty. To reach the Community Hubs, visit www.oercommons.org/hubs/openstax.

#### Technology partners

As allies in making high-quality learning materials accessible, our technology partners offer optional low-cost tools that are integrated with OpenStax books. To access the technology options for your text, visit your book page on openstax.org.

## About the Authors

### Senior Contributing Author

**Jay Abramson, Arizona State University**

Jay Abramson has been teaching Precalculus for over 35 years, the last 20 at Arizona State University, where he is a principal lecturer in the School of Mathematics and Statistics. His accomplishments at ASU include co-developing the university’s first hybrid and online math courses as well as an extensive library of video lectures and tutorials. In addition, he has served as a contributing author for two of Pearson Education’s math programs, NovaNet Precalculus and Trigonometry. Prior to coming to ASU, Jay taught at Texas State Technical College and Amarillo College. He received Teacher of the Year awards at both institutions.

### Contributing Authors

Valeree Falduto, Palm Beach State College

Rachael Gross, Towson University

David Lippman, Pierce College

Melonie Rasmussen, Pierce College

Rick Norwood, East Tennessee State University

Nicholas Belloit, Florida State College Jacksonville

Jean-Marie Magnier, Springfield Technical Community College

Harold Whipple

Christina Fernandez

### Reviewers

Phil Clark, Scottsdale Community College

Michael Cohen, Hofstra University

Charles Conrad, Volunteer State Community College

David French, Tidewater Community College

Matthew Goodell, SUNY Ulster

Lance Hemlow, Raritan Valley Community College

Dongrin Kim, Arizona State University

Cynthia Landrigan, Eerie Community College

Wendy Lightheart, Lane Community College

Chinenye Ofodile, Albany State University

Carl Penziul, Tompkins-Cortland Community College

Sandra Nite, Texas A&M University

Eugenia Peterson, Richard J. Daley College

Rhonda Porter, Albany State University

Michael Price, University of Oregon

Steven Purtee, Valencia College

William Radulovich, Florida State College Jacksonville

Camelia Salajean, City Colleges of Chicago

Katy Shields, Oakland Community College

Nathan Schrenk, ECPI University

Pablo Suarez, Delaware State University

Allen Wolmer, Atlanta Jewish Academy

The following faculty contributed to the development of OpenStax *Precalculus*, the text from which this product was updated and derived.

**Precalculus Reviewers**

Nina Alketa, Cecil College

Kiran Bhutani, Catholic University of America

Brandie Biddy, Cecil College

Lisa Blank, Lyme Central School

Bryan Blount, Kentucky Wesleyan College

Jessica Bolz, The Bryn Mawr School

Sheri Boyd, Rollins College

Sarah Brewer, Alabama School of Math and Science

Charles Buckley, St. Gregory’s University

Michael Cohen, Hofstra University

Kenneth Crane, Texarkana College

Rachel Cywinski, Alamo Colleges

Nathan Czuba

Srabasti Dutta, Ashford University

Kristyanna Erickson, Notre Dame of Maryland University

Nicole Fernandez, Georgetown University / Kent State University

David French, Tidewater Community College

Douglas Furman, SUNY Ulster

Lance Hemlow, Raritan Valley Community College

Erinn Izzo, Nicaragua Christian Academy

John Jaffe

Jerry Jared, Blue Ridge School

Stan Kopec, Mount Wachusett Community College

Kathy Kovacs

Cynthia Landrigan, Erie Community College

Sara Lenhart, Christopher Newport University

Wendy Lightheart, Lane Community College

Joanne Manville, Bunker Hill Community College

Karla McCavit, Albion College

Cynthia McGinnis, Northwest Florida State College

Lana Neal, University of Texas at Austin

Rhonda Porter, Albany State University

Steven Purtee, Valencia College

William Radulovich, Florida State College Jacksonville

Alice Ramos, Bethel College

Nick Reynolds, Montgomery Community College

Amanda Ross, A. A. Ross Consulting and Research, LLC

Erica Rutter, Arizona State University

Sutandra Sarkar, Georgia State University

Willy Schild, Wentworth Institute of Technology

Todd Stephen, Cleveland State University

Scott Sykes, University of West Georgia

Linda Tansil, Southeast Missouri State University

John Thomas, College of Lake County

Diane Valade, Piedmont Virginia Community College

Allen Wolmer, Atlanta Jewish Academy