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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.

Additional resources

Student and instructor resources

We’ve compiled additional resources for both students and instructors, including Getting Started Guides, instructor solution manual, 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.

Partner resources

OpenStax Partners are our allies in the mission to make high-quality learning materials affordable and accessible to students and instructors everywhere. Their tools integrate seamlessly with our OpenStax titles at a low cost. To access the partner resources for your text, visit your book page on openstax.org.

About the authors

Lead author, senior content expert

Jay Abramson has been teaching Precalculus 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 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.
Honorable Mention
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
Kristy Erickson, Cecil College
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

Questions & Answers

prove that [a+b, b+c, c+a]= 2[a b c]
Ashutosh Reply
can't prove
Akugry
i can prove [a+b+b+c+c+a]=2[a+b+c]
this is simple
Akugry
hi
Stormzy
x exposant 4 + 4 x exposant 3 + 8 exposant 2 + 4 x + 1 = 0
HERVE Reply
x exposent4+4x exposent3+8x exposent2+4x+1=0
HERVE
How can I solve for a domain and a codomains in a given function?
Oliver Reply
ranges
EDWIN
Thank you I mean range sir.
Oliver
proof for set theory
Kwesi Reply
don't you know?
Inkoom
find to nearest one decimal place of centimeter the length of an arc of circle of radius length 12.5cm and subtending of centeral angle 1.6rad
Martina Reply
factoring polynomial
Noven Reply
what's your topic about?
Shin Reply
find general solution of the Tanx=-1/root3,secx=2/root3
Nani Reply
find general solution of the following equation
Nani
the value of 2 sin square 60 Cos 60
Sanjay Reply
0.75
Lynne
0.75
Inkoom
when can I use sin, cos tan in a giving question
duru Reply
depending on the question
Nicholas
I am a carpenter and I have to cut and assemble a conventional roof line for a new home. The dimensions are: width 30'6" length 40'6". I want a 6 and 12 pitch. The roof is a full hip construction. Give me the L,W and height of rafters for the hip, hip jacks also the length of common jacks.
John
I want to learn the calculations
Koru Reply
where can I get indices
Kojo Reply
I need matrices
Nasasira
hi
Raihany
Hi
Solomon
need help
Raihany
maybe provide us videos
Nasasira
about complex fraction
Raihany
Hello
Cromwell
a
Amie
What do you mean by a
Cromwell
nothing. I accidentally press it
Amie
you guys know any app with matrices?
Khay
Ok
Cromwell
Solve the x? x=18+(24-3)=72
Leizel Reply
x-39=72 x=111
Suraj
Solve the formula for the indicated variable P=b+4a+2c, for b
Deadra Reply
Need help with this question please
Deadra
b=-4ac-2c+P
Denisse
b=p-4a-2c
Suddhen
b= p - 4a - 2c
Snr
p=2(2a+C)+b
Suraj
b=p-2(2a+c)
Tapiwa
P=4a+b+2C
COLEMAN
b=P-4a-2c
COLEMAN
like Deadra, show me the step by step order of operation to alive for b
John
A laser rangefinder is locked on a comet approaching Earth. The distance g(x), in kilometers, of the comet after x days, for x in the interval 0 to 30 days, is given by g(x)=250,000csc(π30x). Graph g(x) on the interval [0, 35]. Evaluate g(5)  and interpret the information. What is the minimum distance between the comet and Earth? When does this occur? To which constant in the equation does this correspond? Find and discuss the meaning of any vertical asymptotes.
Kaitlyn Reply

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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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