# College Algebra and Trigonometry

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## 0321227638

• Edition: 3rd
• Format: Hardcover
• Copyright: 2009-01-01
• Publisher: Addison Wesley
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### Summary

Focusing on helping students to develop both the conceptual understanding and the analytical skills necessary to experience success in mathematics, we present each mathematical topic in this text using a carefully developed learning system to actively engage students in the learning process. We have tried to address the diverse needs of today's students through a more open design, updated figures and graphs, helpful features, careful explanations of topics, and a comprehensive package of supplements and study aids. Students will benefit from the text's student-oriented approach. We believe instructors will particularly welcome the new Annotated Instructor's Edition, which provides answers in the margin to almost all exercises, plus helpful Teaching Tips.

### Table of Contents

Preface x
Supplements Guide xv
 R Review of Basic Concepts
1(84)
 R.1 Real Numbers and Their Properties
2(14)
 Sets of Numbers and the Number Line
 Exponents
 Order of Operations
 Properties of Real Numbers
 R.2 Order and Absolute Value
16(8)
 Order on the Number Line
 Absolute Value
 Properties of Absolute Value
 R.3 Polynomials
24(13)
 Rules for Exponents
 Polynomials
 Addition and Subtraction Multiplication
 Division
 R.4 Factoring Polynomials
37(9)
 Factoring Out the Greatest Common Factor
 Factoring by Grouping
 Factoring Trinomials
 Factoring Binomials
 Factoring by Substitution
 R.5 Rational Expressions
46(9)
 Rational Expressions
 Lowest Terms of a Rational Expression
 Multiplication and Division
 Addition and Subtraction
 Complex Fractions
 R.6 Rational Exponents
55(10)
 Negative Exponents and the Quotient Rule
 Rational Exponents
 Complex Fractions Revisited
 R.7 Radical Expressions
65(19)
 Radical Notation
 Simplified Radicals
 Operations with Radicals
 Rationalizing Denominators
 Summary
76(3)
 Review Exercises
79(4)
 Test
83(1)
 Quantitative Reasoning
84(1)
 1 Equations and Inequalities
85(96)
 1.1 Linear Equations
86(6)
 Basic Terminology of Equations
 Solving Linear Equations
 Identities, Conditional Equations, and Contradictions
 Solving for a Specified Variable (Literal Equations)
 1.2 Applications and Modeling with Linear Equations
92(15)
 Solving Applied Problems
 Geometry Problems
 Motion Problems
 Work Rate Problems
 Mixture Problems
 Modeling with Linear Equations
 1.3 Complex Numbers
107(8)
 Basic Concepts of Complex Numbers
 Operations on Complex Numbers
 1.4 Quadratic Equations
115(10)
 Solving a Quadratic Equation
 Completing the Square
 The Quadratic Formula
 Solving for a Specified Variable
 The Discriminant
 1.5 Applications and Modeling with Quadratic Equations
125(11)
 Geometry Problems
 Using the Pythagorean Theorem
 Height of a Propelled Object
 Modeling with Quadratic Equations
 1.6 Other Types of Equations
136(10)
 Rational Equations
 Equations with Radicals
 Equations Quadratic in Form
 Summary Exercises on Solving Equations
146(21)
 1.7 Inequalities
146(14)
 Linear Inequalities
 Three-Part Inequalities
 Quadratic Inequalities
 Rational Inequalities
 1.8 Absolute Value Equations and Inequalities
160(20)
 Absolute Value Equations
 Absolute Value Inequalities
 Special Cases
 Absolute Value Models for Distance and Tolerance
 Summary
167(4)
 Review Exercises
171(7)
 Test
178(2)
 Quantitative Reasoning
180(1)
 2 Graphs and Functions
181(112)
 2.1 Graphs of Equations
182(15)
 Ordered Pairs
 The Rectangular Coordinate System
 The Distance Formula
 The Midpoint Formula
 Graphing Equations
 Circles
 2.2 Functions
197(17)
 Relations and Functions
 Domain and Range
 Determining Functions from Graphs or Equations
 Function Notation
 Increasing, Decreasing, and Constant Functions
 2.3 Linear Functions
214(13)
 Graphing Linear Functions
 Standard Form Ax + By = C
 Slope
 Average Rate of Change
 Linear Models
 2.4 Equations of Lines; Curve Fitting
227(14)
 Point-Slope Form
 Slope-Intercept Form
 Vertical and Horizontal Lines
 Parallel and Perpendicular Lines
 Modeling Data
 Solving Linear Equations in One Variable by Graphing
 Summary Exercises on Graphs, Functions, and Equations
241(40)
 2.5 Graphs of Basic Functions
242(11)
 Continuity
 The Identity, Squaring, and Cubing Functions
 The Square Root and Cube Root Functions
 The Absolute Value Function
 Piecewise-Defined Functions
 The Relation x = y2
 2.6 Graphing Techniques
253(15)
 Stretching and Shrinking
 Reflecting
 Symmetry
 Even and Odd Functions
 Translations
 2.7 Function Operations and Composition
268(24)
 Arithmetic Operations on Functions
 The Difference Quotient
 Composition of Functions
 Summary
281(4)
 Review Exercises
285(5)
 Test
290(2)
 Quantitative Reasoning
292(1)
 3 Polynomial and Rational Functions
293(96)
 3.1 Quadratic Functions and Models
294(19)
 Quadratic Functions
 Graphing Techniques
 Completing the Square
 The Vertex Formula
 Quadratic Models and Curve Fitting
 3.2 Synthetic Division
313(7)
 Synthetic Division
 Evaluating Polynomial Functions Using the Remainder Theorem
 Testing Potential Zeros
 3.3 Zeros of Polynomial Functions
320(11)
 Factor Theorem
 Rational Zeros Theorem
 Number of Zeros
 Conjugate Zeros Theorem
 Finding Zeros of a Polynomial Function
 Descartes' Rule of Signs
 3.4 Polynomial Functions: Graphs, Applications, and Models
331(18)
 Graphs of f(x) = axn
 Graphs of General Polynomial Functions
 Turning Points and End Behavior
 Graphing Techniques
 Intermediate Value and Boundedness Theorems
 Approximating Real Zeros
 Polynomial Models and Curve Fitting
 Summary Exercises on Polynomial Functions, Zeros, and Graphs
349(28)
 3.5 Rational Functions: Graphs, Applications, and Models
350(19)
 The Reciprocal Function f(x) = 1/x
 The Function f(x) = 1/x²
 Asymptotes
 Steps for Graphing Rational Functions
 Rational Function Models
 3.6 Variation
369(19)
 Direct Variation
 Inverse Variation
 Combined and Joint Variation
 Summary
377(4)
 Review Exercises
381(5)
 Test
386(2)
 Quantitative Reasoning
388(1)
 4 Exponential and Logarithmic Functions
389(84)
 4.1 Inverse Functions
390(12)
 Inverse Operations
 One-to-One Functions
 Inverse Functions
 Equations of Inverses
 An Application of Inverse Functions to Cryptography
 4.2 Exponential Functions
402(16)
 Exponents and Properties
 Exponential Functions
 Exponential Equations
 Compound Interest
 The Number e and Continuous Compounding
 Exponential Models and Curve Fitting
 4.3 Logarithmic Functions
418(13)
 Logarithms
 Logarithmic Equations
 Logarithmic Functions
 Properties of Logarithms
 Summary Exercises on Inverse, Exponential, and Logarithmic Functions
431(33)
 4.4 Evaluating Logarithms and the Change-of-Base Theorem
432(11)
 Common Logarithms
 Applications and Modeling with Common Logarithms
 Natural Logarithms
 Applications and Modeling with Natural Logarithms
 Logarithms to Other Bases
 4.5 Exponential and Logarithmic Equations
443(9)
 Exponential Equations
 Logarithmic Equations
 Applications and Modeling
 4.6 Applications and Models of Exponential Growth and Decay
452(20)
 The Exponential Growth or Decay Function
 Growth Function Models
 Decay Function Models
 Summary
464(3)
 Review Exercises
467(4)
 Test
471(1)
 Quantitative Reasoning
472(1)
 5 Trigonometric Functions
473(60)
 5.1 Angles
474(7)
 Basic Terminology
 Degree Measure
 Standard Position
 Coterminal Angles
 5.2 Trigonometric Functions
481(14)
 Trigonometric Functions
 Quadrantal Angles
 Reciprocal Identities
 Signs and Ranges of Function Values
 Pythagorean Identities
 Quotient Identities
 5.3 Evaluating Trigonometric Functions
495(14)
 Definitions of the Trigonometric Functions
 Trigonometric Function Values of Special Angles
 Reference Angles
 Special Angles as Reference Angles
 Finding Function Values with a Calculator
 Finding Angle Measures
 5.4 Solving Right Triangles
509(22)
 Significant Digits
 Solving Triangles
 Angles of Elevation or Depression
 Bearing
 Further Applications
 Summary
524(3)
 Review Exercises
527(3)
 Test
530(1)
 Quantitative Reasoning
531(2)
 6 The Circular Functions and Their Graphs
533(72)
 6.1 Radian Measure
534(11)
 Radian Measure
 Converting Between Degrees and Radians
 Arc Length of a Circle
 Area of a Sector of a Circle
 6.2 The Unit Circle and Circular Functions
545(11)
 Circular Functions
 Finding Values of Circular Functions
 Determining a Number with a Given Circular Function Value
 Angular and Linear Speed
 6.3 Graphs of the Sine and Cosine Functions
556(19)
 Periodic Functions
 Graph of the Sine Function
 Graph of the Cosine Function
 Graphing Techniques, Amplitude, and Period
 Translations
 Combinations of Translations
 Determining a Trigonometric Model Using Curve Fitting
 6.4 Graphs of the Other Circular Functions
575(13)
 Graphs of the Cosecant and Secant Functions
 Graphs of the Tangent and Cotangent Functions
 Addition of Ordinates
 Summary Exercises on Graphing Circular Functions
588(5)
 6.5 Harmonic Motion
588(15)
 Simple Harmonic Motion
 Damped Oscillatory Motion
 Summary
593(3)
 Review Exercises
596(5)
 Test
601(2)
 Quantitative Reasoning
603(2)
 7 Trigonometric Identities and Equations
605(80)
 7.1 Fundamental Identities
606(6)
 Negative-Angle Identities
 Fundamental Identities
 Using the Fundamental Identities
 7.2 Verifying Trigonometric Identities
612(9)
 Verifying Identities by Working with One Side
 Verifying Identities by Working with Both Sides
 7.3 Sum and Difference Identities
621(11)
 Cosine Sum and Difference Identities
 Cofunction Identities
 Sine and Tangent Sum and Difference Identities
 7.4 Double-Angle Identities and Half-Angle Identities
632(12)
 Double-Angle Identities
 Product-to-Sum and Sum-to-Product Identities
 Half-Angle Identities
 Summary Exercises on Verifying Trigonometric Identities
644(32)
 7.5 Inverse Circular Functions
645(13)
 Inverse Functions
 Inverse Sine Function
 Inverse Cosine Function
 Inverse Tangent Function
 Remaining Inverse Circular Functions
 Inverse Function Values
 7.6 Trigonometric Equations
658(12)
 Solving by Linear Methods
 Solving by Factoring
 Solving by Quadratic Methods
 Solving by Using Trigonometric Identities
 Equations with Half-Angles
 Equations with Multiple Angles
 Applications
 7.7 Equations Involving Inverse Trigonometric Functions
670(14)
 Solving for x in Terms of y Using Inverse Functions
 Solving Inverse Trigonometric Equations
 Summary
676(3)
 Review Exercises
679(3)
 Test
682(2)
 Quantitative Reasoning
684(1)
 8 Applications of Trigonometry
685(98)
 8.1 The Law of Sines
686(15)
 Congruency and Oblique Triangles
 Derivation of the Law of Sines a Applications
 Ambiguous Case
 Area of a Triangle
 8.2 The Law of Cosines
701(13)
 Derivation of the Law of Cosines
 Applications
 Heron's Formula for the Area of a Triangle
 8.3 Vectors, Operations, and the Dot Product
714(10)
 Basic Terminology
 Algebraic Interpretation of Vectors
 Operations with Vectors
 Dot Product and the Angle Between Vectors
 8.4 Applications of Vectors
724(7)
 The Equilibrant
 Incline Applications
 Navigation Applications
 Summary Exercises on Applications of Trigonometry and Vectors
731(38)
 8.5 Trigonometric (Polar) Form of Complex Numbers; Products and Quotients
732(10)
 The Complex Plane and Vector Representation
 Trigonometric (Polar) Form
 Products of Complex Numbers in Trigonometric Form
 Quotients of Complex Numbers in Trigonometric Form
 8.6 De Moivre's Theorem; Powers and Roots of Complex Numbers
742(7)
 Powers of Complex Numbers (De Moivre's Theorem)
 Roots of Complex Numbers
 8.7 Polar Equations and Graphs
749(12)
 Polar Coordinate System
 Graphs of Polar Equations
 Converting from Polar to Rectangular Equations
 Classifying Polar Equations
 8.8 Parametric Equations, Graphs, and Applications
761(20)
 Basic Concepts
 Parametric Graphs and Their Rectangular Equivalents
 The Cycloid
 Applications of Parametric Equations
 Summary
769(4)
 Review Exercises
773(6)
 Test
779(2)
 Quantitative Reasoning
781(2)
 9 Systems and Matrices
783(108)
 9.1 Systems of Linear Equations
784(17)
 Linear Systems
 Substitution Method
 Elimination Method
 Special Systems
 Applying Systems of Equations
 Solving Linear Systems with Three Unknowns (Variables)
 Using Systems of Equations to Model Data
 9.2 Matrix Solution of Linear Systems
801(12)
 The Gauss-Jordan Method
 Special Systems
 9.3 Determinant Solution of Linear Systems
813(11)
 Determinants
 Cofactors
 Evaluating n X n Determinants
 Cramer's Rule
 9.4 Partial Fractions
824(6)
 Decomposition of Rational Expressions
 Distinct Linear Factors
 Repeated Linear Factors
 Distinct Linear and Quadratic Factors
 Repeated Quadratic Factors
 9.5 Nonlinear Systems of Equations
830(11)
 Solving Nonlinear Systems with Real Solutions
 Solving Nonlinear Systems with Nonreal Complex Solutions
 Applying Nonlinear Systems
 Summary Exercises on Systems of Equations
841(38)
 9.6 Systems of Inequalities and Linear Programming
842(11)
 Solving Linear Inequalities
 Solving Systems of Inequalities
 Linear Programming
 9.7 Properties of Matrices
853(14)
 Basic Definitions
 Adding Matrices
 Special Matrices
 Subtracting Matrices
 Multiplying Matrices
 Applying Matrix Algebra
 9.8 Matrix Inverses
867(12)
 Identity Matrices
 Multiplicative Inverses
 Solving Systems Using Inverse Matrices
 Summary
879(5)
 Review Exercises
884(4)
 Test
888(2)
 Quantitative Reasoning
890(1)
10 Analytic Geometry 891(44)
 10.1 Parabolas
892(10)
 Conic Sections
 Horizontal Parabolas
 Geometric Definition and Equations of Parabolas
 An Application of Parabolas
 10.2 Ellipses
902(11)
 Equations and Graphs of Ellipses
 Translated Ellipses
 Eccentricity
 Applications of Ellipses
 10.3 Hyperbolas
913(8)
 Equations and Graphs of Hyperbolas
 Translated Hyperbolas
 Eccentricity
 10.4 Summary of the Conic Sections
921(7)
 Characteristics
 Identifying Conic Sections
 Geometric Definition of Conic Sections
 Summary
928(2)
 Review Exercises
930(2)
 Test
932(2)
 Quantitative Reasoning
934(1)
11 Further Topics in Algebra 935(78)
 11.1 Sequences and Series
936(11)
 Sequences
 Series and Summation Notation
 Summation Properties
 11.2 Arithmetic Sequences and Series
947(9)
 Arithmetic Sequences
 Arithmetic Series
 11.3 Geometric Sequences and Series
956(11)
 Geometric Sequences
 Geometric Series
 Infinite Geometric Series
 Annuities
 Summary Exercises on Sequences and Series
967(1)
 11.4 The Binomial Theorem
968(8)
 A Binomial Expansion Pattern
 Pascal's Triangle
 n-Factorial
 Binomial Coefficients
 The Binomial Theorem
 kth Term of a Binomial Expansion
 11.5 Mathematical Induction
976(6)
 Proof by Mathematical Induction
 Proving Statements
 Generalized Principle of Mathematical Induction
 Proof of the Binomial Theorem
 11.6 Counting Theory
982(11)
 Fundamental Principle of Counting
 Permutations
 Combinations
 Distinguishing Between Permutations and Combinations
 11.7 Basics of Probability
993(11)
 Basic Concepts
 Complements and Venn Diagrams
 Odds
 Union of Two Events
 Binomial Probability
 Summary
1004(4)
 Review Exercises
1008(3)
 Test
1011(1)
 Quantitative Reasoning
1012(1)
Appendix A Polar Form of Conic Sections 1013(4)
Appendix B Rotation of Axes 1017(6)
Appendix C Geometry Formulas 1022 Glossary 1023
Solutions to Selected Exercises S-1
Answers to Selected Exercises A-1
Index of Applications I-1
Index I-7