Algebra with Trigonometry for College Students (with CD-ROM, Make the Grade, and InfoTrac)

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  • Edition: 5th
  • Format: Hardcover
  • Copyright: 12/20/2001
  • Publisher: Cengage Learning
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This text, written by best-selling developmental mathematics author Pat McKeague, features a more streamlined review of elementary algebra, allowing for earlier coverage of intermediate topics. An early introduction to graphing presents the foundation for a wide variety of graphing problems throughout the text. Early coverage of functions helps students feel comfortable with the many examples and graphs of functions that occur in later chapters. The first ten chapters of this book cove the topics usually found in a college-level algebra course. The last three chapters cover the essential topics from trigonometry. Optional technology sections and integrated throughout text as a way for students to better understand the material being discussed.

Table of Contents

Preface to the Instructorp. vi
Preface to the Studentp. xiii
Basic Properties and Definitionsp. 1
Fundamental Definitions and Notationp. 3
Properties of Real Numbersp. 16
Arithmetic With Real Numbersp. 27
Exponents and Scientific Notationp. 38
Polynomials, Sums, Differences, and Productsp. 49
Factoringp. 61
Special Factoringp. 70
Recognizing Patternsp. 79
Summaryp. 90
Reviewp. 94
Testp. 96
Projectsp. 97
Equations and Inequalities in One Variablep. 99
Linear and Quadratic Equations in One Variablep. 101
Formulasp. 112
Applicationsp. 126
Linear Inequalities in One Variablep. 143
Equations With Absolute Valuep. 154
Inequalities Involving Absolute Valuep. 159
Summaryp. 167
Reviewp. 169
Testp. 171
Cumulative Reviewp. 172
Projectsp. 173
Equations and Inequalities in Two Variablesp. 176
Paired Data and the Rectangular Coordinate Systemp. 178
The Slope of a Linep. 192
The Equation of a Linep. 202
Linear Inequalities in Two Variablesp. 215
Introduction to Functionsp. 223
Function Notationp. 236
Algebra With Functionsp. 247
Variationp. 254
Summaryp. 266
Reviewp. 269
Testp. 270
Cumulative Reviewp. 271
Projectsp. 272
Systems of Linear Equations and Inequalitiesp. 274
Systems of Linear Equations in Two Variablesp. 276
Systems of Linear Equations in Three Variablesp. 289
Introduction to Determinantsp. 298
Cramer's Rulep. 306
Applicationsp. 312
Systems of Linear Inequalitiesp. 327
Summaryp. 336
Reviewp. 339
Testp. 340
Cumulative Reviewp. 341
Projectsp. 343
Rational Expressions and Rational Functionsp. 345
Basic Properties and Reducing to Lower Termsp. 347
Division of Polynomialsp. 360
Multiplication and Division of Rational Expressionsp. 371
Addition and Subtraction of Rational Expressionsp. 380
Complex Fractionsp. 389
Equations Involving Rational Expressionsp. 394
Applicationsp. 405
Summaryp. 417
Reviewp. 419
Testp. 420
Cumulative Reviewp. 421
Projectsp. 422
Rational Exponents and Rootsp. 424
Rational Exponentsp. 426
More Expressions Involving Rational Exponentsp. 438
Simplified Form for Radicalsp. 445
Addition and Subtraction of Radical Expressionsp. 457
Multiplication and Division of Radical Expressionsp. 461
Equations With Radicalsp. 468
Complex Numbersp. 478
Summaryp. 486
Reviewp. 488
Testp. 489
Cumulative Reviewp. 490
Projectsp. 491
Quadratic Functionsp. 493
Completing the Squarep. 494
The Quadratic Formulap. 505
Additional Items Involving Solutions to Equationsp. 516
Equations Quadratic in Formp. 526
Graphing Parabolasp. 535
Quadratic Inequalitiesp. 549
Summaryp. 560
Reviewp. 561
Testp. 562
Cumulative Reviewp. 563
Projectsp. 564
Exponential and Logarithmic Functionsp. 566
Exponential Functionsp. 567
The Inverse of a Functionp. 578
Logarithms Are Exponentsp. 588
Properties of Logarithmsp. 597
Common Logarithms and Natural Logarithmsp. 602
Exponential Equations and Change of Basep. 611
Summaryp. 620
Reviewp. 621
Testp. 623
Cumulative Reviewp. 623
Projectsp. 624
Sequences and Seriesp. 627
Sequencesp. 628
Seriesp. 637
Arithmetic Sequencesp. 644
Geometric Sequencesp. 651
The Binomial Expansionp. 661
Summaryp. 669
Reviewp. 671
Testp. 672
Cumulative Reviewp. 673
Projectsp. 674
Conic Sectionsp. 676
The Circlep. 677
Ellipses and Hyperbolasp. 686
Second-Degree Inequalities and Nonlinear Systemsp. 700
Summaryp. 708
Reviewp. 709
Testp. 710
Cumulative Reviewp. 710
Projectsp. 711
Introduction to Trigonometryp. 713
Degrees, Radians, and Special Trianglesp. 714
Trigonometric Functionsp. 724
Trigonometric Functions and Calculatorsp. 731
Graphing I: Amplitude and Periodp. 743
Graphing II: Phase Shiftp. 758
Finding an Equation from Its Graphp. 768
Inverse Trigonometric Functionsp. 779
Summaryp. 785
Reviewp. 788
Testp. 790
Cumulative Reviewp. 791
Projectsp. 793
Trigonometric Identities and Equationsp. 795
Introduction to Identitiesp. 796
Proving Identitiesp. 804
Sum and Difference Formulasp. 809
Double-Angle and Half-Angle Formulasp. 817
Solving Trigonometric Equationsp. 823
Summaryp. 830
Reviewp. 832
Testp. 833
Cumulative Reviewp. 833
Projectsp. 835
Trianglesp. 837
Definition II: Right Triangle Trigonometryp. 838
The Law of Sinesp. 851
The Ambiguous Casep. 857
The Law of Cosinesp. 862
Summaryp. 868
Reviewp. 870
Testp. 871
Cumulative Reviewp. 871
Projectsp. 873
Synthetic Divisionp. 1
Matrix Solutions to Linear Systemsp. 1
Conditional Statementsp. 1
Answers to Odd-Numbered Problems, Chapter Reviews, Chapter Tests, and Cumulative Reviewsp. 1
Indexp. 1
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