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Precalculus: Concepts Through Functions, A Right Triangle Approach to Trigonometry,9780131874763
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Precalculus: Concepts Through Functions, A Right Triangle Approach to Trigonometry

by ;
ISBN13:

9780131874763

ISBN10:
0131874764
Format:
Hardcover
Pub. Date:
1/1/2007
Publisher(s):
Prentice Hall

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Summary

This new text embodies Sullivan/Sullivanrs"s hallmarks - accuracy, precision, depth, strong student support, and abundant exerciseswhile exposing students early (Chapter One) to the study of functionsand taking aright triangle approachto trigonometry."IT WORKS"for instructors and students because it focuses students on thefundamentals:preparingfor class,practicingtheir homework, andreviewing. After completing the book, students will be prepared to handle the algebra found in subsequent courses such as finite mathematics, business mathematics, and engineering calculus and will have a solid understanding of the concept of a function.

Table of Contents

Preface to the Instructorp. xiii
List of Applicationsp. xix
Photo Creditsp. xxiii
To the Studentp. xxiv
Foundations: A Prelude To Functionsp. 1
The Distance and Midpoint Formulasp. 2
Graphs of Equations in Two Variables; Intercepts; Symmetryp. 8
Linesp. 18
Circlesp. 33
Functions and Their Graphsp. 39
Functionsp. 40
The Graph of a Functionp. 54
Properties of Functionsp. 63
Library of Functions; Piecewise-defined Functionsp. 75
Graphing Techniques: Transformationsp. 85
Mathematical Models: Constructing Functionsp. 97
Chapter Reviewp. 105
Chapter Testp. 111
Chapter Projectsp. 112
Linear and Quadratic Functionsp. 113
Properties of Linear Functionsp. 114
Building Linear Functions from Data; Direct Variationp. 125
Quadratic Functions and Their Zerosp. 133
Properties of Quadratic Functionsp. 144
Inequalities Involving Quadratic Functionsp. 154
Quadratic Modelsp. 158
Complex Zeros of a Quadratic Functionp. 167
Equations and Inequalities Involving the Absolute Value Functionp. 170
Chapter Reviewp. 175
Chapter Testp. 179
Chapter Projectsp. 179
Cumulative Reviewp. 180
Polynomial and Rational Functionsp. 181
Polynomial Functions and Modelsp. 182
Properties of Rational Functionsp. 203
The Graph of a Rational Function; Inverse and Joint Variationp. 213
Polynomial and Rational Inequalitiesp. 231
The Real Zeros of a Polynomial Functionp. 236
Complex Zeros; Fundamental Theorem of Algebrap. 250
Chapter Reviewp. 256
Chapter Testp. 259
Chapter Projectsp. 260
Cumulative Reviewp. 261
Exponential and Logarithmic Functionsp. 263
Composite Functionsp. 264
One-to-One Functions; Inverse Functionsp. 271
Exponential Functionsp. 284
Logarithmic Functionsp. 300
Properties of Logarithmsp. 312
Logarithmic and Exponential Equationsp. 320
Compound Interestp. 325
Exponential Growth and Decay; Newton's Law; Logistic Growth and Decayp. 334
Building Exponential, Logarithmic, and Logistic Functions from Datap. 345
Chapter Reviewp. 353
Chapter Testp. 359
Chapter Projectsp. 359
Cumulative Reviewp. 360
Trigonometric Functionsp. 361
Angles and Their Measurep. 362
Right Triangle Trigonometryp. 375
Computing the Values of Trigonometric Functions of Acute Anglesp. 386
Trigonometric Functions of General Anglesp. 397
Unit Circle Approach; Properties of the Trigonometric Functionsp. 407
Graphs of the Sine and Cosine Functionsp. 418
Graphs of the Tangent, Cotangent, Cosecant, and Secant Functionsp. 433
Phase Shift; Sinusoidal Curve Fittingp. 439
Chapter Reviewp. 450
Chapter Testp. 456
Chapter Projectsp. 457
Cumulative Reviewp. 458
Analytic Trigonometryp. 459
The Inverse Sine, Cosine, and Tangent Functionsp. 460
The Inverse Trigonometric Functions (Continued)p. 472
Trigonometric Identitiesp. 477
Sum and Difference Formulasp. 485
Double-angle and Half-angle Formulasp. 494
Product-to-Sum and Sum-to-Product Formulasp. 503
Trigonometric Equations (I)p. 507
Trigonometric Equations (II)p. 613
Chapter Reviewp. 520
Chapter Testp. 524
Chapter Projectsp. 524
Cumulative Reviewp. 525
Applications of Trigonometric Functionsp. 527
Applications Involving Right Trianglesp. 528
The Law of Sinesp. 533
The Law of Cosinesp. 544
Area of a Trianglep. 550
Simple Harmonic Motion; Damped Motion; Combining Wavesp. 555
Chapter Reviewp. 564
Chapter Testp. 568
Chapter Projectsp. 569
Cumulative Reviewp. 570
Polar Coordinates; Vectorsp. 571
Polar Coordinatesp. 572
Polar Equations and Graphsp. 580
The Complex Plane; De Moivre's Theoremp. 596
Vectorsp. 604
The Dot Productp. 615
Vectors in Spacep. 623
The Cross Productp. 632
Chapter Reviewp. 638
Chapter Testp. 642
Chapter Projectsp. 643
Cumulative Reviewp. 644
Analytic Geometryp. 645
Conicsp. 646
The Parabolap. 647
The Ellipsep. 656
The Hyperbolap. 666
Rotation of Axes; General Form of a Conicp. 678
Polar Equations of Conicsp. 686
Plane Curves and Parametric Equationsp. 692
Chapter Reviewp. 704
Chapter Testp. 707
Chapter Projectsp. 707
Cumulative Reviewp. 708
Systems of Equations and Inequalitiesp. 709
Systems of Linear Equations: Substitution and Eliminationp. 710
Systems of Linear Equations: Matricesp. 724
Systems of Linear Equations: Determinantsp. 739
Matrix Algebrap. 749
Partial Fraction Decompositionp. 765
Systems of Nonlinear Equationsp. 772
Systems of Inequalitiesp. 781
Linear Programmingp. 789
Chapter Reviewp. 796
Chapter Testp. 801
Chapter Projectsp. 802
Cumulative Reviewp. 803
Sequences; Induction; The Binomial Theoremp. 805
Sequencesp. 806
Arithmetic Sequencesp. 815
Geometric Sequences; Geometric Seriesp. 820
Mathematical Inductionp. 831
The Binomial Theoremp. 834
Chapter Reviewp. 841
Chapter Testp. 843
Chapter Projectsp. 844
Cumulative Reviewp. 844
Counting and Probabilityp. 895
Sets and Countingp. 846
Permutations and Combinationsp. 851
Probabilityp. 861
Chapter Reviewp. 871
Chapter Testp. 874
Chapter Projectsp. 875
Cumulative Reviewp. 875
A Preview of Calculus: The Limit, Derivative, and Integral of a Functionp. 877
Finding Limits Using Tables and Graphsp. 878
Algebra Techniques for Finding Limitsp. 883
One-sided Limits; Continuous Functionsp. 890
The Tangent Problem; The Derivativep. 897
The Area Problem; The Integralp. 905
Chapter Reviewp. 911
Chapter Testp. 915
Chapter Projectsp. 916
Reviewp. 1
Algebra Essentialsp. 1
Geometry Essentialsp. 11
Polynomialsp. 19
Factoring Polynomialsp. 29
Synthetic Divisionp. 38
Rational Expressionsp. 41
nth Roots; Rational Exponentsp. 52
Solving Equationsp. 60
Interval Notation; Solving Inequalitiesp. 66
Problem Solving: Applications of Linear Equationsp. 74
Complex Numbersp. 82
Graphing Utilitiesp. 1
The Viewing Rectanglep. 1
Using a Graphing Utility to Graph Equationsp. 3
Using a Graphing Utility to Locate Intercepts and Check for Symmetryp. 7
Using a Graphing Utility to Solve Equationsp. 9
Square Screensp. 11
Using a Graphing Utility to Graph Inequalitiesp. 12
Using a Graphing Utility to Solve Systems of Linear Equationsp. 14
Using a Graphing Utility to Graph a Polar Equationp. 15
Using a Graphing Utility to Graph Parametric Equationsp. 16
Answersp. 1
Indexp. 1
Table of Contents provided by Ingram. All Rights Reserved.


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