College Algebra and Trigonometry

by Lial, Margaret L.; Hornsby, John; Schneider, David I.

• ISBN13: 9780321227638
• ISBN10: 0321227638
• Edition: 3rd
• Format: Hardcover
• Copyright: 2009-01-01
• Publisher: Addison Wesley

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