Algebra and Trigonometry [RENTAL EDITION]

1323 Pages·2021·126.285 MB·English

by  Robert F. Blitzer

This is a special edition of an established title widely used by colleges and
GLOBAL GLOBAL
universities throughout the world. Pearson published this exclusive edition
for the benefit of students outside the United States and Canada. If you
EDITION EDITION
purchased this book within the United States or Canada, you should be aware EG
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that it has been imported without the approval of the Publisher or Author. ITO
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Blitzer’s Algebra and Trigonometry helps students of varying mathematics backgrounds acquire a solid
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foundation in algebra and trigonometry, preparing them for courses such as calculus, business calculus,
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and finite mathematics. Maintaining the previous editions’ engaging approach, the seventh edition g
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continues to show students how algebra and trigonometry can model and solve authentic real-world
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problems and continues to enhance students’ problem-solving skills and critical thinking.
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Key Features
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• Blitzer’s distinctive and relatable voice engages students in the world of mathematics through n
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compelling real-word applications like modeling COVID-19 cases using polynomial functions,

solving a dual investment problem, and responding to negative life events. T
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• Ninety-seven worked-out examples and exercises based on new data sets and 168
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updated examples and exercises involve topics relevant to college students, such as student g
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loan debts, the wage gap between men and women, and the cost of tuition at public and private
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colleges.
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• Blitzer Bonus essays provide historical and interdisciplinary connections to the algebra and m
trigonometry under study, showing students that mathematics is a fascinating and dynamic
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discipline.
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• Great Question! boxes present a variety of study tips that anticipate student questions. Answers
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to these questions point out common errors to avoid, offer suggestions for problem solving, and
provide informal hints and suggestions.
• End-of-chapter Review Exercises followed by a Chapter Test enable students to test their
understanding of the material covered. Beginning with Chapter 2, each chapter concludes with a
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comprehensive collection of Cumulative Review Exercises. DE
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Available separately for purchase is MyLab Math for Algebra and Trigonometry, the teaching and learning O
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platform that empowers instructors to personalize learning for every student. New section-level NH

Video Assignments are especially helpful for online classes or “flipped” classes, where some or all
learning takes place independently. The newly added, gradable GeoGebra Graphing Exercises
enable students to interact directly with graphs in a manner that reflects how they would graph on Trigonometry
paper. When combined with Pearson’s trusted educational content, this optional suite helps deliver B
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the desired learning outcomes. t
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SEVENTH EDITION
ROBERT F. BLITZER
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A Brief Guide to Getting the Most from This Book
GRAPHS OF TRIGONOMETRIC FUNCTIONS
y
y y
y = sin x y = cos x 4
1 Read the Book 1 1 y = tan x
2
–p
x x x
Feature Description Benefit –p p 3p –p p 2p p 2p
2 2 2
–2
Section-Opening Every section opens with a scenario Realizing that algebra and trigonometry are
–1 –1
Scenarios presenting a unique application of everywhere will help motivate your learning.
–4
algebra or trigonometry in your life (See page 136.)
outside the classroom. Domain: all real numbers, Domain: all real numbers, Domain: all real numbers
p
(–∞, ∞) (–∞, ∞) except odd multiples of
2
Examples are clearly written and The blue annotations will help you Range: [–1, 1] Range: [–1, 1] Range: all real numbers
EXAMPLE
provide step-by-step solutions. No understand the solutions by providing the Period: 2p Period: 2p Period: p
steps are omitted, and each step is reason why every algebraic or trigonometric 1 1
y = csc x = y = sec x =
y y = cot x y sin x y cos x
thoroughly explained to the right of the step is true. (See page 138.)
mathematics.
4 4 4
Applications Using Interesting applications from nearly Ever wondered how you’ll use algebra
2 2 2
Real-World Data every discipline, supported by and trigonometry? This feature will show
up-to-date real-world data, are you how they can solve real problems. x x x
included in every section. (See pages 294–296.) –p p 3p p –p p 2p
2 2 2 2
–2
Answers to students’ questions offer By seeing common mistakes, you’ll be able
GREAT QUESTION
suggestions for problem solving, point to avoid them. This feature should help –4
out common errors to avoid, and you not to feel anxious or threatened when
Domain: all real numbers Domain: all real numbers Domain: all real numbers
provide informal hints and suggestions. asking questions in class. (See page 139.) except integral multiples of p except integral multiples of p except odd multiples ofp
2
Range: all real numbers Range: (–∞, –1] ∪ [1, ∞) Range: (–∞, –1] ∪ [1, ∞)
Brief Reviews cover skills you already Having these refresher boxes easily
BRIEF REVIEW Period: p Period: 2p Period: 2p
learned but may have forgotten. accessible will help ease anxiety about
FUNDAMENTAL TRIGONOMETRIC IDENTITIES Double-Angle Formulas
skills you may have forgotten.
sin 2u = 2 sin u cos u
(See page 508.) 1 1
Reciprocal Identities sin x = csc x csc x = sin x cos 2u = cos2 u - sin2 u = 2 cos2 u - 1 = 1 - 2 sin2 u
2 tan u
BLITZER BONUS These enrichment essays provide Yet even more proof that math is an cos x = se1c x sec x = co1s x tan 2u = 1 - tan2 u
historical, interdisciplinary, and interesting and dynamic discipline! 1 1 Power-Reducing Formulas
tan x = cot x =
otherwise interesting connections to the (See page 195.) cot x tan x 1 - cos 2u 1 + cos 2u 1 - cos 2u
sin2 u = cos2 u = tan2 u =
algebra or trigonometry under study. sin x cos x 2 2 1 + cos 2u
Quotient Identities tan x = cot x =
cos x sin x Half-Angle Formulas
Voice balloons help to demystify algebra Does math ever look foreign to you? This Pythagorean Identities sin2 x + cos2 x = 1 a 1 - cos a a 1 + cos a
sin = { cos = {
and trigonometry. They translate math feature often translates math into everyday 1 + tan2 x = sec2 x 2 2 2 2
B B
into plain English, clarify problem- English. (See page 193.) 1 + cot2 x = csc2 x tana = { 1 - cos a = 1 - cos a = sin a
solving procedures, and present Even-Odd Identities 2 1 + cos a sin a 1 + cos a
alternative ways of understanding. sin(-x) = -sin x cos(-x) = cos x tan(-x) = -tan x OBLIQUE TRIANGLBES
csc(-x) = -csc x sec(-x) = sec x cot(-x) = -cot x C
WHAT YOU'LL LEARN Every section begins with a list of The objectives focus your reading by
OTHER TRIGONOMETRIC IDENTITIES
1 LOebajerncitnivge oinb tjhecet miveasrg. iEna wchh eorbe jethceti voeb jies crteivseta itse d ewmheprhea tsoiz fiinngd wit.h (aSt eise mpaogste i m17p8o.r)tant and Sum and Difference Formulas b a
sin(a + b) = sin a cos b + cos a sin b
covered.
sin(a - b) = sin a cos b - cos a sin b
The screens displayed in the Even if you are not using a graphing cos(a + b) = cos a cos b - sin a sin b A c B
TECHNOLOGY technology boxes show how graphing utility in the course, this feature will help cos(a - b) = cos a cos b + sin a sin b a b c
utilities verify and visualize algebraic or you understand different approaches to tan a + tan b Law of Sines sin A = sin B = sin C
tan(a + b) =
trigonometric results. problem solving. (See page 140.) 1 - tan a tan b Law of Cosines a2 = b2 + c2 - 2bc cos A
tan(a - b) = tan a - tan b b2 = a2 + c2 - 2ac cos B
1 + tan a tan b c2 = a2 + b2 - 2ab cos C
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2 Work the Problems
Feature Description Benefit
Each example is followed by a You learn best by doing. You’ll solidify your
CHECK POINT
matched problem, called a Check understanding of worked examples if you
Point, that offers you the opportunity try a similar problem right away to be sure
to work a similar exercise. The answers you understand what you’ve just read.
to the Check Points are provided in (See page 138.)
the answer section.
Achieving Success boxes offer Follow these suggestions to help achieve
ACHIEVING SUCCESS
strategies for persistence and success your full academic potential in college
in college mathematics courses. mathematics. (See page 149.)
These short-answer questions, mainly It is difficult to learn algebra and trigonometry
CONCEPT AND
fill-in-the-blank and true/false items, without knowing their special language.
VOCABULARY CHECK
assess your understanding of the These exercises test your understanding
definitions and concepts presented in of the vocabulary and concepts.
each section. (See page 149.)
An abundant collection of exercises The parallel order of the Practice Exercises
EXERCISE SET is included in an Exercise Set at the lets you refer to the worked examples
end of each section. Exercises are and use them as models for solving these
organized within several categories. problems. (See page 150.)
Your instructor will usually provide
guidance on which exercises to work.
The exercises in the first category,
Practice Exercises, follow the same
order as the section’s worked
examples.
Practice PLUS This category of exercises contains It is important to dig in and develop
more challenging problems that often your problem-solving skills. Practice
require you to combine several skills or PLUS Exercises provide you with ample
concepts. opportunity to do so. (See page 437.)
Retaining the Concepts Beginning with Chapter 2, each These exercises improve your
Exercise Set contains review exercises understanding of the topics and help
under the header “Retaining the maintain mastery of the material.
Concepts.” (See page 284.)
Preview Exercises Each Exercise Set concludes with three These exercises let you review previously
problems to help you prepare for the covered material that you’ll need to be
next section. successful for the forthcoming section.
Some of these problems will get you
thinking about concepts you’ll soon
encounter. (See page 153.)
A01_BLIT3447_07_GE_FM.indd 1 08/06/22 08:19
3 Review for Quizzes and Tests
Feature Description Benefit
Mid-Chapter Check Point At approximately the midway point in By combining exercises from the first
the chapter, an integrated set of review half of the chapter, the Mid-Chapter
exercises allows you to review the skills Check Points give a comprehensive
and concepts you learned separately review before you move on to the
over several sections. material in the remainder of the
chapter. (See page 311.)
Chapter Review Chart Each chapter contains a review chart Review this chart and you’ll know the
that summarizes the definitions and most important material in the chapter!
concepts in every section of the (See page 236.)
chapter. Examples that illustrate these
key concepts are also referenced in the
chart.
A comprehensive collection of review Practice makes perfect. These
Chapter Review
exercises for each of the chapter’s exercises contain the most significant
Exercise Set
sections follows the review chart. problems for each of the chapter’s
sections. (See page 239.)
Chapter Test Each chapter contains a practice You can use the chapter test to
test with approximately 25 problems determine whether you have mastered
that cover the important concepts in the material covered in the chapter.
the chapter. Take the practice test, (See page 243.)
check your answers, and then watch
the Chapter Test Prep Videos to see
worked-out solutions for any exercises
you miss.
Chapter Test Prep Videos These videos contain worked-out The videos let you review any
solutions to every exercise in each exercises you miss on the
chapter test and can be found in chapter test.
MyLab Math and on YouTube at
youtube.com/user/pearsonmathstats
(playlist “Blitzer Algebra and
Trigonometry 7e”).
Objective Videos These fresh, interactive videos walk The videos provide you with active
you through the concepts from every learning at your own pace.
objective of the text.
Cumulative Review Beginning with Chapter 2, each chapter Ever forget what you’ve learned?
concludes with a comprehensive These exercises ensure that you are
collection of mixed cumulative review not forgetting anything as you move
exercises. These exercises combine forward. (See page 373.)
problems from previous chapters
and the present chapter, providing an
ongoing cumulative review.
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7th EDITION
GLOBAL EDITION
Algebra and Trigonometry
Robert Blitzer
Miami Dade College
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© Pearson Education Limited 2023
The rights of Robert Blitzer to be identified as the author of this work have been asserted by him in accordance with
the Copyright, Designs and Patents Act 1988.
Authorized adaptation from the United States edition, entitled Algebra and Trigonometry, 7th Edition, ISBN 978-0-
13-692217-9 by Robert Blitzer published by Pearson Education © 2022.
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Contents
Preface 9
About the Author 18
To the Student 19
Applications Index 21
P Fundamental Concepts
of Algebra 29
P.1 Algebraic Expressions, Mathematical Models,
and Real Numbers 30
P.2 Exponents and Scientific Notation 48
P.3 Radicals and Rational Exponents 63
P.4 Polynomials 79
Mid-Chapter Check Point 90
P.5 Factoring Polynomials 91
P.6 Rational Expressions 103
Summary, Review, and Test 118
Review Exercises 119
Chapter P Test 121
1 Equations and
Inequalities 123
1.1 Graphs and Graphing Utilities 124
1.2 Linear Equations and Rational Equations 136
1.3 Models and Applications 154
1.4 Complex Numbers 168
1.5 Quadratic Equations 178
Mid-Chapter Check Point 201
1.6 Other Types of Equations 203
1.7 Linear Inequalities and Absolute Value
Inequalities 219
Summary, Review, and Test 236
Review Exercises 239
Chapter 1 Test 243
5
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6 Contents
Mid-Chapter Check Point 440
3.5 Rational Functions and Their Graphs 441
3.6 Polynomial and Rational Inequalities 461
3.7 Modeling Using Variation 474
Summary, Review, and Test 484
Review Exercises 487
Chapter 3 Test 490
Cumulative Review Exercises (Chapters 1–3) 492
4 Exponential and Logarithmic
Functions 493
4.1 Exponential Functions 494
4.2 Logarithmic Functions 508
4.3 Properties of Logarithms 523
Mid-Chapter Check Point 533
4.4 Exponential and Logarithmic Equations 534
4.5 Exponential Growth and Decay; Modeling Data 549
Summary, Review, and Test 563
2 Functions
Review Exercises 565
and Graphs 245
Chapter 4 Test 569
2.1 Basics of Functions and Their Graphs 246 Cumulative Review Exercises (Chapters 1–4) 570
2.2 More on Functions and Their Graphs 265
2.3 Linear Functions and Slope 285
2.4 More on Slope 301
Mid-Chapter Check Point 311
2.5 Transformations of Functions 312
2.6 Combinations of Functions; Composite Functions 328
2.7 Inverse Functions 343
2.8 Distance and Midpoint Formulas; Circles 354
Summary, Review, and Test 364
Review Exercises 367
Chapter 2 Test 371
Cumulative Review Exercises (Chapters 1–2) 373
3 Polynomial and Rational
Functions 375
3.1 Quadratic Functions 376
3.2 Polynomial Functions and Their Graphs 394
3.3 Dividing Polynomials; Remainder and Factor
Theorems 412
3.4 Zeros of Polynomial Functions 425
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Contents 7
5 Trigonometric 7.5 Complex Numbers in Polar Form;
Functions 571 DeMoivre’s Theorem 813
7.6 Vectors 826
5.1 Angles and Radian Measure 572
7.7 The Dot Product 841
5.2 Right Triangle Trigonometry 589
Summary, Review, and Test 851
5.3 Trigonometric Functions of Any Angle 606
Review Exercises 854
5.4 Trigonometric Functions of Real Numbers; Periodic
Chapter 7 Test 856
Functions 619
Cumulative Review Exercises (Chapters 1–7) 857
Mid-Chapter Check Point 628
5.5 Graphs of Sine and Cosine Functions 629
5.6 Graphs of Other Trigonometric Functions 650
5.7 Inverse Trigonometric Functions 664
5.8 Applications of Trigonometric Functions 682
Summary, Review, and Test 693
Review Exercises 697
Chapter 5 Test 699
Cumulative Review Exercises (Chapters 1–5) 700
6 Analytic
Trigonometry 701
6.1 Verifying Trigonometric Identities 702
6.2 Sum and Difference Formulas 714
6.3 Double-Angle, Power-Reducing,
and Half-Angle Formulas 725
Mid-Chapter Check Point 736
6.4 Product-to-Sum and Sum-to-Product Formulas 737
6.5 Trigonometric Equations 746
Summary, Review, and Test 761
Review Exercises 762 8 Systems of Equations
Chapter 6 Test 764 and Inequalities 859
Cumulative Review Exercises (Chapters 1–6) 765
8.1 Systems of Linear Equations in Two Variables 860
8.2 Systems of Linear Equations in Three Variables 879
7 Additional Topics
8.3 Partial Fractions 887
in Trigonometry 767
8.4 Systems of Nonlinear Equations in Two Variables 898
7.1 The Law of Sines 768
Mid-Chapter Check Point 908
7.2 The Law of Cosines 780
8.5 Systems of Inequalities 909
7.3 Polar Coordinates 789
8.6 Linear Programming 922
7.4 Graphs of Polar Equations 801
Summary, Review, and Test 929
Mid-Chapter Check Point 812
Review Exercises 931
Chapter 8 Test 934
Cumulative Review Exercises (Chapters 1–8) 934
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8 Contents
9 Matrices and 11.4 Mathematical Induction 1136
Determinants 937 11.5 The Binomial Theorem 1145
11.6 Counting Principles, Permutations, and
9.1 Matrix Solutions to Linear Systems 938
Combinations 1153
9.2 Inconsistent and Dependent Systems
11.7 Probability 1164
and Their Applications 952
Summary, Review, and Test 1179
9.3 Matrix Operations and Their Applications 961
Review Exercises 1181
Mid-Chapter Check Point 976
Chapter 11 Test 1184
9.4 Multiplicative Inverses of Matrices
and Matrix Equations 977 Cumulative Review Exercises (Chapters 1–11) 1185
9.5 Determinants and Cramer’s Rule 991
Appendix: Where Did That Come From? Selected Proofs 1187
Summary, Review, and Test 1004
Answers to Selected Exercises 1193
Review Exercises 1006
Subject Index 1299
Chapter 9 Test 1008
Credits 1317
Cumulative Review Exercises (Chapters 1–9) 1009
10 Conic Sections and
Analytic Geometry 1011
10.1 The Ellipse 1012
10.2 The Hyperbola 1027
10.3 The Parabola 1042
Mid-Chapter Check Point 1056
10.4 Rotation of Axes 1058
10.5 Parametric Equations 1069
10.6 Conic Sections in Polar Coordinates 1079
Summary, Review, and Test 1089
Review Exercises 1092
Chapter 10 Test 1094
Cumulative Review Exercises (Chapters 1–10) 1095
11 Sequences, Induction,
and Probability 1097
11.1 Sequences and Summation Notation 1098
11.2 Arithmetic Sequences 1109
11.3 Geometric Sequences and Series 1120
Mid-Chapter Check Point 1135
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