Cover image for Algebra and trigonometry : enhanced with graphing utilities
Title:
Algebra and trigonometry : enhanced with graphing utilities
Personal Author:
Edition:
2nd ed.
Publication Information:
New Jersey : Prentice Hall, 2000
ISBN:
9780130833341

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30000004740795 QA154.2 S835 2000 Open Access Book Book
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30000004434985 QA154.2 S835 2000 Open Access Book Book
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30000003411307 QA154.2 S835 2000 Open Access Book Book
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Summary

Summary

This text will be useful both to students who have little mathematical background and those who are experienced in the subject and want to continue studying it. Each chapter has a review section with problems and a project section that incorporates real life examples of how the newly learned concept


Table of Contents

Preface to the Instructorp. ix
Preface to the Studentp. xiii
List of Applicationp. xxiii
Photo Creditsp. xxvii
Chapter 1 Graphsp. 1
1.1 Rectangular Coordinates; Graphing Utilities; Scatter Diagramsp. 2
1.2 Graphs of Equationsp. 15
1.3 Solving Equationsp. 29
1.4 Setting Up Equations; Applicationsp. 40
1.5 Solving Inequalitiesp. 53
1.6 Linesp. 66
1.7 Circlesp. 83
Chapter Reviewp. 90
Chapter Projectsp. 95
Chapter 2 Linear and Quadratic Functionsp. 97
2.1 Functionsp. 98
2.2 Linear Functions and Modelsp. 115
2.3 Quadratic Equations and Functionsp. 124
2.4 Quadratic Functions and Modelsp. 139
Chapter Reviewp. 150
Chapter Projectsp. 154
Chapter 3 Functions and Their Graphsp. 155
3.1 Characteristics of Functions; Library of Functionsp. 156
3.2 Graphing Techniques: Transformationsp. 178
3.3 Operations on Functions; Composite Functionsp. 191
3.4 Mathematical Models: Constructing Functionsp. 200
Chapter Reviewp. 208
Chapter Projectsp. 212
Chapter 4 Polynomial and Rational Functionsp. 213
4.1 Power Functions and Modelsp. 214
4.2 Polynomial Functions and Modelsp. 221
4.3 Polynomial Divisionp. 234
4.4 The Real Zeros of a Polynomial Functionp. 240
4.5 Complex Numbers; Quadratic Equations with a Negative Discriminantp. 254
4.6 Complex Zeros; Fundamental Theorem of Algebrap. 263
4.7 Rational Functionsp. 270
4.8 Polynomial and Rational Inequalitiesp. 293
Chapter Reviewp. 302
Chapter Projectsp. 307
Chapter 5 Exponential and Logarithmic Functionsp. 309
5.1 One-to-One Functions; Inverse Functionsp. 310
5.2 Exponential Functionsp. 323
5.3 Logarithmic Functionsp. 337
5.4 Properties of Logarithmsp. 347
5.5 Logarithmic and Exponential Equationsp. 355
5.6 Compound Interestp. 362
5.7 Growth and Decayp. 372
5.8 Exponential, Logarithmic, and Logistic Curve Fittingp. 382
Chapter Reviewp. 393
Chapter Projectsp. 398
Chapter 6 Systems of Equations and Inequalitiesp. 401
6.1 Systems of Linear Equations: Two Equations Containing Two Variablesp. 402
6.2 Systems of Linear Equations: Three Equations Containing Three Variablesp. 413
6.3 Systems of Linear Equations: Matricesp. 419
6.4 Systems of Linear Equations: Determinantsp. 434
6.5 Matrix Algebrap. 445
6.6 Systems of Linear Inequalities; Linear Programmingp. 464
6.7 Partial Fraction Decompositionp. 481
Chapter Reviewp. 488
Chapter Projectsp. 493
Chapter 7 Trigonometric Functionsp. 495
7.1 Angles and Their Measurep. 496
7.2 Right Triangle Trigonometryp. 508
7.3 Computing the Values of Trigonometric Functions of Given Anglesp. 519
7.4 Trigonometric Functions of General Anglesp. 526
7.5 Properties of the Trigonometric Functions; Unit Circle Approachp. 537
7.6 Graphs of the Trigonometric Functionsp. 548
7.7 Sinusoidal Graphs; Sinusoidal Curve Fittingp. 560
Chapter Reviewp. 579
Chapter Projectsp. 585
Chapter 8 Analytic Trigonometryp. 587
8.1 Trigonometric Identitiesp. 589
8.2 Sum and Difference Formulasp. 594
8.3 Double-Angle and Half-Angle Formulasp. 603
8.4 Product-to-Sum and Sum-to-Product Formulasp. 613
8.5 The Inverse Trigonometric Functionsp. 616
8.6 Trigonometric Equations (I)p. 632
8.7 Trigonometric Equations (II)p. 637
Chapter Reviewp. 644
Chapter Projectsp. 648
Chapter 9 Applications of Trigonometric Functionsp. 651
9.1 Solving Right Trianglesp. 652
9.2 The Law of Sinesp. 661
9.3 The Law of Cosinesp. 673
9.4 The Area of a Trianglep. 679
9.5 Simple Harmonic Motion; Damped Motionp. 685
Chapter Reviewp. 692
Chapter Projectsp. 697
Chapter 10 Polar Coordinates; Vectorsp. 699
10.1 Polar Coordinatesp. 700
10.2 Polar Equations and Graphsp. 708
10.3 The Complex Plane; DeMoivre's Theoremp. 728
10.4 Vectorsp. 736
10.5 The Dot Productp. 747
Chapter Reviewp. 757
Chapter Projectsp. 761
Chapter 11 Analytic Geometryp. 763
11.1 Conicsp. 764
11.2 The Parabolap. 765
11.3 The Ellipsep. 777
11.4 The Hyperbolap. 790
11.5 Rotation of Axes; General Form of a Conicp. 804
11.6 Polar Equations of Conicsp. 813
11.7 Plane Curves and Parametric Equationsp. 819
11.8 Systems of Nonlinear Equationsp. 834
Chapter Reviewp. 845
Chapter Projectsp. 849
Chapter 12 Sequences; Induction; The Binomial Theoremp. 851
12.1 Sequencesp. 852
12.2 Arithmetic Sequencesp. 864
12.3 Geometric Sequences; Geometric Seriesp. 871
12.4 Mathematical Inductionp. 887
12.5 The Binomial Theoremp. 891
Chapter Reviewp. 898
Chapter Projectsp. 902
Chapter 13 Counting and Probabilityp. 905
13.1 Sets and Countingp. 906
13.2 Permutations and Combinationsp. 912
13.3 Probability of Equally Likely Outcomesp. 922
13.4 Analyzing Univariate Data; Obtaining Probabilities from Datap. 938
Chapter Reviewp. 952
Chapter Projectsp. 957
Appendix Reviewp. 959
1. Real Numbersp. 959
2. Algebra Reviewp. 973
3. Geometry Reviewp. 984
4. Integer Exponentsp. 990
5. Polynomialsp. 998
6. Factoring Polynomialsp. 1006
7. Rational Expressionsp. 1015
8. Square Roots; Radicalsp. 1027
9. Rational Exponentsp. 1035
Answersp. 1
Indexp. 1