Table Of ContentAlgebra and Trigonometry
senior contributing author
Jay abramson, arizona state University
About Our Team
Senior Contributing Author
Jay Abramson has been teaching Algebra and Trigonometry for 33 years, the last 14 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 uni-
versity’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 The following faculty contributed to the development of OpenStax
Valeree Falduto, Palm Beach State College Precalculus, the text from which this product was updated and derived.
Rachael Gross, Towson University
Honorable Mention
David Lippman, Pierce College
Nina Alketa, Cecil College
Melonie Rasmussen, Pierce College
Kiran Bhutani, Catholic University of America
Rick Norwood, East Tennessee State University
Brandie Biddy, Cecil College
Nicholas Belloit, Florida State College Jacksonville
Lisa Blank, Lyme Central School
Jean-Marie Magnier, Springfield Technical Community College
Bryan Blount, Kentucky Wesleyan College
Harold Whipple
Jessica Bolz, The Bryn Mawr School
Christina Fernandez
Sheri Boyd, Rollins College
Reviewers Sarah Brewer, Alabama School of Math and Science
Phil Clark, Scottsdale Community College Charles Buckley, St. Gregory's University
Michael Cohen, Hofstra University Michael Cohen, Hofstra University
Charles Conrad, Volunteer State Community College Kenneth Crane, Texarkana College
David French, Tidewater Community College Rachel Cywinski, Alamo Colleges
Matthew Goodell, SUNY Ulster Nathan Czuba
Lance Hemlow, Raritan Valley Community College Srabasti Dutta, Ashford University
Dongrin Kim, Arizona State University Kristy Erickson, Cecil College
Cynthia Landrigan, Eerie Community College Nicole Fernandez, Georgetown University / Kent State University
Wendy Lightheart, Lane Community College David French, Tidewater Community College
Chinenye Ofodile, Albany State University Douglas Furman, SUNY Ulster
Carl Penziul, Tompkins-Cortland Community College Lance Hemlow, Raritan Valley Community College
Sandra Nite, Texas A&M University Erinn Izzo, Nicaragua Christian Academy
Eugenia Peterson, Richard J. Daley College John Jaffe
Rhonda Porter, Albany State University Jerry Jared, Blue Ridge School
Michael Price, University of Oregon Stan Kopec, Mount Wachusett Community College
Steven Purtee, Valencia College Kathy Kovacs
William Radulovich, Florida State College Jacksonville Cynthia Landrigan, Erie Community College
Camelia Salajean, City Colleges of Chicago Sara Lenhart, Christopher Newport University
Katy Shields, Oakland Community College Wendy Lightheart, Lane Community College
Nathan Schrenk, ECPI University Joanne Manville, Bunker Hill Community College
Pablo Suarez, Delaware State University Karla McCavit, Albion College
Allen Wolmer, Atlanta Jewish Academy 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
OpenStax
OpenStax provides free, peer-reviewed, openly licensed textbooks for introductory college and Advanced Placement® courses
and low-cost, personalized courseware that helps students learn. A nonprofit ed tech initiative based at Rice University,
we’re committed to helping students access the tools they need to complete their courses and meet their educational goals.
Rice University
OpenStax and OpenStax CNX are initiatives of Rice University. As a leading research university with a distinctive
commitment to undergraduate education, Rice University aspires to path-breaking research, unsurpassed teaching, and
contributions to the betterment of our world. It seeks to fulfill this mission by cultivating a diverse community of learning
and discovery that produces leaders across the spectrum of human endeavor.
Foundation Support
OpenStax is grateful for the tremendous support of our sponsors. Without their strong engagement, the goal of free access
to high-quality textbooks would remain just a dream.
Laura and John Arnold Foundation (LJAF) actively seeks opportunities to invest in organizations
and thought leaders that have a sincere interest in implementing fundamental changes that not
only yield immediate gains, but also repair broken systems for future generations. LJAF currently
focuses its strategic investments on education, criminal justice, research integrity, and public
accountability.
The William and Flora Hewlett Foundation has been making grants since 1967 to help solve
social and environmental problems at home and around the world. The Foundation concentrates
its resources on activities in education, the environment, global development and population,
performing arts, and philanthropy, and makes grants to support disadvantaged communities in
the San Francisco Bay Area.
Guided by the belief that every life has equal value, the Bill & Melinda Gates Foundation works
to help all people lead healthy, productive lives. In developing countries, it focuses on improving
people’s health with vaccines and other life-saving tools and giving them the chance to lift
themselves out of hunger and extreme poverty. In the United States, it seeks to significantly
improve education so that all young people have the opportunity to reach their full potential.
Based in Seattle, Washington, the foundation is led by CEO Jeff Raikes and Co-chair William H.
Gates Sr., under the direction of Bill and Melinda Gates and Warren Buffett.
The Maxfield Foundation supports projects with potential for high impact in science, education,
sustainability, and other areas of social importance.
Our mission at The Michelson 20MM Foundation is to grow access and success by eliminating
unnecessary hurdles to affordability. We support the creation, sharing, and proliferation of
more effective, more affordable educational content by leveraging disruptive technologies, open
educational resources, and new models for collaboration between for-profit, nonprofit, and public
THE MICHELSON 20MM
FOUNDATION entities.
Calvin K. Kazanjian was the founder and president of Peter Paul (Almond Joy), Inc. He firmly
believed that the more people understood about basic economics the happier and more prosperous
they would be. Accordingly, he established the Calvin K. Kazanjian Economics Foundation Inc,
in 1949 as a philanthropic, nonpolitical educational organization to support efforts that enhanced
economic understanding.
The Bill and Stephanie Sick Fund supports innovative projects in the areas of Education, Art,
Science and Engineering
OpenStax - If you redistribute part of this textbook, then you must display on every
digital format page view (including but not limited to EPUB, PDF, and
Rice University
HTML) and on every physical printed page the following attribution:
6100 Main Street MS-375
"Download for free at https://openstax.org/details/books/algebra-and-
Houston, Texas 77005
trigonometry."
To learn more about OpenStax, visit http://openstax.org.
- If you use this textbook as a bibliographic reference, please include
Individual print copies and bulk orders can be purchased through our https://openstax.org/details/books/algebra-and-trigonometry in your
website. citation."
© 2017 Rice University. Textbook content produced by OpenStax The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax
is licensed under a Creative Commons Attribution 4.0 International
CNX name, OpenStax CNX logo, OpenStax Tutor name, Openstax Tutor
License (CC BY 4.0). Under this license, any user of this textbook or the
logo, Connexions name, Connexions logo, Rice University name, and
textbook contents herein must provide proper attribution as follows:
Rice University logo are not subject to the license and may not be repro-
- If you redistribute this textbook in a digital format (including but not duced without the prior and express written consent of Rice University.
limited to EPUB, PDF, and HTML), then you must retain on every page
view the following attribution: "Download for free at https://openstax. For questions regarding this license, please contact
org/details/books/algebra-and-trigonometry." [email protected].
- If you redistribute this textbook in a print format, then you must
include on every physical page the following attribution: "Download for
PRINT ISBN-10 1-938168-37-2
free at https://openstax.org/details/books/algebra-and-trigonometry.
PRINT ISBN-13 978-1-938168-37-6
PDF ISBN-10 1-947172-10-7
PDF ISBN-13 978-1-947172-10-4
Revision AT-2015-002(03/17)-BW
Original Publication Year: 2015
Study where you want, what
you want, when you want.
When you access College Success in our web view, you can use our new online
highlighting and note-taking features to create your own study guides.
Our books are free and flexible, forever.
Get started at openstax.org/details/books/algebra-and-trigonometry
Access. The future of education.
openstax.org
Brief Contents
1
Prerequisites 1
2
Equations and Inequalities 73
3
Functions 159
4
Linear Functions 279
5
Polynomial and Rational Functions 343
6
Exponential and Logarithmic Functions 463
7
The Unit Circle: Sine and Cosine Functions 575
8
Periodic Functions 641
9
Trigonometric Identities and Equations 695
10
Further Applications of Trigonometry 761
11
Systems of Equations and Inequalities 875
12
Analytic Geometry 981
13
Sequences, Probability and Counting Theory 1055
i
