,Algebra and
Trigonometry 4 th
EDITION
Judith A. Beecher
Indiana University Purdue University Indianapolis
Judith A. Penna
Indiana University Purdue University Indianapolis
Marvin L. Bittinger
Indiana University Purdue University Indianapolis
Addison-Wesley
Boston Columbus Indianapolis
New York San Francisco Upper Saddle River
Amsterdam Cape Town Dubai London
Madrid Milan Munich Paris Montréal Toronto
Delhi Mexico City São Paulo Sydney
Hong Kong Seoul Singapore Taipei Tokyo
, Editor-in-Chief Anne Kelly
Executive Content Editor Christine O’Brien
Senior Content Editor Joanne Dill
Editorial Assistant Brendan Berger
Senior Managing Editor Karen Wernholm
Senior Production Project Manager Kathleen A. Manley
Design Manager Andrea Nix
Senior Design Specialist Heather Scott
Digital Assets Manager Marianne Groth
Supplements Production Coordinator Kerri McQueen
Media Producer Shana Siegmund
Software Development Kristina Evans, MathXL; Mary Durnwald, TestGen
Executive Marketing Manager Roxanne McCarley
Marketing Manager Peggy Sue Lucas
Marketing Assistant Katherine Minton
Senior Author Support/Technology Specialist Joe Vetere
Senior Manufacturing Buyer Carol Melville
Senior Media Buyer Ginny Michaud
Design, Art Editing, and Photo Research The Davis Group, Inc.
Editorial Coordination Martha Morong/Quadrata, Inc.
Production Coordination Sally Lifland/Lifland et al., Bookmakers
Composition PreMediaGlobal
Illustrations Network Graphics, William Melvin, and PreMediaGlobal
Cover Image Shutterstock/©medvedeff
Photo credits can be found on p. 989. NOTICE:
This work is
Many of the designations used by manufacturers and sellers to distinguish their products are protected by United
claimed as trademarks. Where those designations appear in this book, and Pearson was aware of States copyright laws
a trademark claim, the designations have been printed in initial caps or all caps. and is provided solely
Library of Congress Cataloging-in-Publication Data for the use of instruc-
tors in teaching their
Beecher, Judith A. courses and assessing
Algebra and trigonometry / Judith A. Beecher, Judith A. Penna, Marvin L. Bittinger.—4th ed. student learning.
p. cm. Dissemination or sale
ISBN-13: 978-0-321-69398-3 of any part of this
work (including on
ISBN-10: 0-321-69398-1
the World Wide Web)
1. Algebra—Textbooks. 2. Trigonometry—Textbooks. I. Penna, Judith A. will destroy the
II. Bittinger, Marvin L. III. Title. integrity of the work
QA152.3.B42 2012 and is not permitted.
512’.13—dc22 2010034358 The work and materi-
als from it should
Copyright © 2012, 2008, 2005, 2002 Pearson Education, Inc. All rights reserved. No part of this
never be made avail-
publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by able to students
any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior except by instructors
written permission of the publisher. Printed in the United States of America. For information on using the accompany-
obtaining permission for use of material in this work, please submit a written request to Pearson ing text in their
Education, Inc., Rights and Contracts Department, 501 Boylston Street, Suite 900, Boston, MA classes. All recipi-
02116, fax your request to 617-671-3447, or e-mail at ents of this work are
expected to abide by
http://www.pearsoned.com/legal/permissions.htm.
these restrictions and
1 2 3 4 5 6 7 8 9 10—DOW—14 13 12 11 10 to honor the intended
pedagogical purposes
and the needs of other
instructors who rely
on these materials.
ISBN-13: 978-0-321-69398-3
ISBN-10: 0-321-69398-1
, Contents
Preface xi
R Basic Concepts of Algebra 1
R.1 The Real-Number System 2
Real Numbers / Interval Notation / Properties of the Real Numbers /
Absolute Value
R.2 Integer Exponents, Scientific Notation, and Order of Operations 8
Integers as Exponents / Scientific Notation / Order of Operations
R.3 Addition, Subtraction, and Multiplication of Polynomials 17
Polynomials / Addition and Subtraction / Multiplication
R.4 Factoring 22
Terms with Common Factors / Factoring by Grouping / Trinomials of the Type
x 2 + bx + c / Trinomials of the Type ax 2 + bx + c, a Z 1 / Special Factorizations
R.5 The Basics of Equation Solving 31
Linear Equations and Quadratic Equations / Formulas
R.6 Rational Expressions 36
The Domain of a Rational Expression / Simplifying, Multiplying, and Dividing
Rational Expressions / Adding and Subtracting Rational Expressions /
Complex Rational Expressions
R.7 Radical Notation and Rational Exponents 45
Simplifying Radical Expressions / An Application / Rationalizing Denominators or
Numerators / Rational Exponents
Study Guide 53
Review Exercises 54
Chapter Test 56
1 Graphs, Functions, and Models 59
1.1 Introduction to Graphing 60
Graphs / Solutions of Equations / Graphs of Equations / The Distance Formula /
Midpoints of Segments / Circles
VISUALIZING THE GRAPH 71
1.2 Functions and Graphs 75
Functions / Notation for Functions / Graphs of Functions / Finding Domains of
Functions / Visualizing Domain and Range / Applications of Functions
CONTENTS iii
Trigonometry 4 th
EDITION
Judith A. Beecher
Indiana University Purdue University Indianapolis
Judith A. Penna
Indiana University Purdue University Indianapolis
Marvin L. Bittinger
Indiana University Purdue University Indianapolis
Addison-Wesley
Boston Columbus Indianapolis
New York San Francisco Upper Saddle River
Amsterdam Cape Town Dubai London
Madrid Milan Munich Paris Montréal Toronto
Delhi Mexico City São Paulo Sydney
Hong Kong Seoul Singapore Taipei Tokyo
, Editor-in-Chief Anne Kelly
Executive Content Editor Christine O’Brien
Senior Content Editor Joanne Dill
Editorial Assistant Brendan Berger
Senior Managing Editor Karen Wernholm
Senior Production Project Manager Kathleen A. Manley
Design Manager Andrea Nix
Senior Design Specialist Heather Scott
Digital Assets Manager Marianne Groth
Supplements Production Coordinator Kerri McQueen
Media Producer Shana Siegmund
Software Development Kristina Evans, MathXL; Mary Durnwald, TestGen
Executive Marketing Manager Roxanne McCarley
Marketing Manager Peggy Sue Lucas
Marketing Assistant Katherine Minton
Senior Author Support/Technology Specialist Joe Vetere
Senior Manufacturing Buyer Carol Melville
Senior Media Buyer Ginny Michaud
Design, Art Editing, and Photo Research The Davis Group, Inc.
Editorial Coordination Martha Morong/Quadrata, Inc.
Production Coordination Sally Lifland/Lifland et al., Bookmakers
Composition PreMediaGlobal
Illustrations Network Graphics, William Melvin, and PreMediaGlobal
Cover Image Shutterstock/©medvedeff
Photo credits can be found on p. 989. NOTICE:
This work is
Many of the designations used by manufacturers and sellers to distinguish their products are protected by United
claimed as trademarks. Where those designations appear in this book, and Pearson was aware of States copyright laws
a trademark claim, the designations have been printed in initial caps or all caps. and is provided solely
Library of Congress Cataloging-in-Publication Data for the use of instruc-
tors in teaching their
Beecher, Judith A. courses and assessing
Algebra and trigonometry / Judith A. Beecher, Judith A. Penna, Marvin L. Bittinger.—4th ed. student learning.
p. cm. Dissemination or sale
ISBN-13: 978-0-321-69398-3 of any part of this
work (including on
ISBN-10: 0-321-69398-1
the World Wide Web)
1. Algebra—Textbooks. 2. Trigonometry—Textbooks. I. Penna, Judith A. will destroy the
II. Bittinger, Marvin L. III. Title. integrity of the work
QA152.3.B42 2012 and is not permitted.
512’.13—dc22 2010034358 The work and materi-
als from it should
Copyright © 2012, 2008, 2005, 2002 Pearson Education, Inc. All rights reserved. No part of this
never be made avail-
publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by able to students
any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior except by instructors
written permission of the publisher. Printed in the United States of America. For information on using the accompany-
obtaining permission for use of material in this work, please submit a written request to Pearson ing text in their
Education, Inc., Rights and Contracts Department, 501 Boylston Street, Suite 900, Boston, MA classes. All recipi-
02116, fax your request to 617-671-3447, or e-mail at ents of this work are
expected to abide by
http://www.pearsoned.com/legal/permissions.htm.
these restrictions and
1 2 3 4 5 6 7 8 9 10—DOW—14 13 12 11 10 to honor the intended
pedagogical purposes
and the needs of other
instructors who rely
on these materials.
ISBN-13: 978-0-321-69398-3
ISBN-10: 0-321-69398-1
, Contents
Preface xi
R Basic Concepts of Algebra 1
R.1 The Real-Number System 2
Real Numbers / Interval Notation / Properties of the Real Numbers /
Absolute Value
R.2 Integer Exponents, Scientific Notation, and Order of Operations 8
Integers as Exponents / Scientific Notation / Order of Operations
R.3 Addition, Subtraction, and Multiplication of Polynomials 17
Polynomials / Addition and Subtraction / Multiplication
R.4 Factoring 22
Terms with Common Factors / Factoring by Grouping / Trinomials of the Type
x 2 + bx + c / Trinomials of the Type ax 2 + bx + c, a Z 1 / Special Factorizations
R.5 The Basics of Equation Solving 31
Linear Equations and Quadratic Equations / Formulas
R.6 Rational Expressions 36
The Domain of a Rational Expression / Simplifying, Multiplying, and Dividing
Rational Expressions / Adding and Subtracting Rational Expressions /
Complex Rational Expressions
R.7 Radical Notation and Rational Exponents 45
Simplifying Radical Expressions / An Application / Rationalizing Denominators or
Numerators / Rational Exponents
Study Guide 53
Review Exercises 54
Chapter Test 56
1 Graphs, Functions, and Models 59
1.1 Introduction to Graphing 60
Graphs / Solutions of Equations / Graphs of Equations / The Distance Formula /
Midpoints of Segments / Circles
VISUALIZING THE GRAPH 71
1.2 Functions and Graphs 75
Functions / Notation for Functions / Graphs of Functions / Finding Domains of
Functions / Visualizing Domain and Range / Applications of Functions
CONTENTS iii
