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College Algebra and Trigonometry

ISBN: 9780321227638 | 0321227638
Edition: 4th
Format: Hardcover
Publisher: Addison Wesley
Pub. Date: 1/1/2009

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SummaryTable of Contents
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.
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Prefacex
Supplements Guidexv
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 Geometry891(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 Algebra935(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 Sections1013(4)
Appendix B Rotation of Axes1017(6)
Appendix C Geometry Formulas 1022 Glossary1023
Solutions to Selected ExercisesS-1
Answers to Selected ExercisesA-1
Index of ApplicationsI-1
IndexI-7

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