College Algebra and Trigonometry 7th Edition by Margaret L. Lial, ISBN-13: 978-0135924549

College Algebra and Trigonometry 7th Edition by Margaret L. Lial, ISBN-13: 978-0135924549

[PDF eBook eTextbook]

• Publisher: ‎ Pearson; 7th edition (February 8, 2020)
• Language: ‎ English
• 1232 pages(Large File: 80 MB)
  
• ISBN-10: ‎ 0135924545
• ISBN-13: ‎ 978-0135924549

For courses in College Algebra & Trigonometry.

Solid support for an evolving course

The College Algebra series by Lial, Hornsby, Schneider, and Daniels combines the experience of master teachers to help students develop the balance of conceptual understanding and analytical skills needed to succeed in mathematics. For this revision, integrated review is now available  for every title in the series, to accommodate varying levels of student preparation. The Review chapter has been expanded to cover the basic algebra concepts that students often find most challenging.

Table of Contents:

Contents
Preface
Welcome to the 7th Edition
Features of this Text
Get the most out of MyLab Math
Preparedness
Integrated Review in MyLab Math
Updated! Videos
Updated! MyNotes and MyClassroomExamples
New! Enhanced Sample Assignments
Resources for Success
Instructor Resources
Student Resources
R Review of Basic Concepts
R.1 Fractions, Decimals, and Percents
Lowest Terms of a Fraction
Improper Fractions and Mixed Numbers
Operations with Fractions
Decimals as Fractions
Operations with Decimals
Fractions as Decimals
Percents as Decimals and Decimals as Percents
Percents as Fractions and Fractions as Percents
Concept Preview
Concept Preview
R.2 Sets and Real Numbers
Basic Definitions
Operations on Sets
Sets of Numbers and the Number Line
Concept Preview
Concept Preview
R.3 Real Number Operations and Properties
Order on the Number Line
Absolute Value
Operations on Real Numbers
Exponents
Order of Operations
Properties of Real Numbers
Concept Preview
Concept Preview
R.4 Integer and Rational Exponents
Product Rule for Exponents
Power Rules for Exponents
Zero as an Exponent
Negative Exponents and the Quotient Rule
Rational Exponents
Concept Preview
Concept Preview
R.5 Polynomials
Polynomials
Addition and Subtraction
Multiplication
Division
Check
Concept Preview
Concept Preview
R.6 Factoring Polynomials
Factoring Out the Greatest Common Factor
Check
Check
Factoring by Grouping
Check
Factoring Trinomials
Check
Check
Check
Factoring Binomials
Check
Factoring by Substitution
Factoring Expressions with Negative or Rational Exponents
Check
Concept Preview
Concept Preview
R.7 Rational Expressions
Rational Expressions
Lowest Terms of a Rational Expression
Multiplication and Division
Addition and Subtraction
Complex Fractions
Concept Preview
Concept Preview
R.8 Radical Expressions
Radical Notation
Simplified Radicals
Operations with Radicals
Rationalizing Denominators
Concept Preview
Concept Preview
Concept Preview
Chapter R Test Prep
Key Terms
R.1
R.2
R.3
R.5
R.6
R.7
R.8
New Symbols
Quick Review
Chapter R Review Exercises
Chapter R Test
1 Equations and Inequalities
1.1 Linear Equations
Basic Terminology of Equations
Linear Equations
Identities, Conditional Equations, and Contradictions
Solving for a Specified Variable (Literal Equations)
Concept Preview
Concept Preview
1.2 Applications and Modeling with Linear Equations
Solving Applied Problems
Geometry Problems
Motion Problems
Mixture Problems
Modeling with Linear Equations
Concept Preview
1.3 Complex Numbers
Basic Concepts of Complex Numbers
Operations on Complex Numbers
Concept Preview
Concept Preview
1.4 Quadratic Equations
The Zero-Factor Property
The Square Root Property
Completing the Square
The Quadratic Formula
Solving for a Specified Variable
The Discriminant
Concept Preview
Concept Preview
1.5 Applications and Modeling with Quadratic Equations
Geometry Problems
The Pythagorean Theorem
Height of a Projected Object
Modeling with Quadratic Equations
Concept Preview
1.6 Other Types of Equations and Applications
Rational Equations
Work Rate Problems
Equations with Radicals
Equations with Rational Exponents
Equations Quadratic in Form
Concept Preview
Concept Preview
1.7 Inequalities
Linear Inequalities
Three-Part Inequalities
Quadratic Inequalities
Rational Inequalities
Concept Preview
1.8 Absolute Value Equations and Inequalities
Basic Concepts
Absolute Value Equations
Absolute Value Inequalities
Special Cases
Absolute Value Models for Distance and Tolerance
Concept Preview
Chapter 1 Test Prep
Key Terms
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
New Symbols
Quick Review
Chapter 1 Review Exercises
Chapter 1 Test
2 Graphs and Functions
2.1 Rectangular Coordinates and Graphs
Ordered Pairs
The Rectangular Coordinate System
The Distance Formula
The Midpoint Formula
Equations in Two Variables
Concept Preview
Concept Preview
Concept Check
2.2 Circles
Center-Radius Form
General Form
An Application
Concept Preview
Concept Preview
Concept Preview
2.3 Functions
Relations and Functions
Domain and Range
Determining Whether Relations Are Functions
Function Notation
Increasing, Decreasing, and Constant Functions
Concept Preview
2.4 Linear Functions
Basic Concepts of Linear Functions
Standard Form Ax+By=C
Slope
Average Rate of Change
Linear Models
Concept Preview
Concept Preview
2.5 Equations of Lines and Linear Models
Point-Slope Form
Slope-Intercept Form
Vertical and Horizontal Lines
Parallel and Perpendicular Lines
Modeling Data
Graphical Solution of Linear Equations in One Variable
Concept Preview
Concept Preview
2.6 Graphs of Basic Functions
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
Concept Preview
2.7 Graphing Techniques
Stretching and Shrinking
Reflecting
Symmetry
Even and Odd Functions
Translations
Concept Preview
2.8 Function Operations and Composition
Arithmetic Operations on Functions
The Difference Quotient
Composition of Functions and Domain
Concept Preview
Concept Preview
Chapter 2 Test Prep
Key Terms
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
New Symbols
Quick Review
Chapter 2 Review Exercises
Chapter 2 Test
3 Polynomial and Rational Functions
3.1 Quadratic Functions and Models
Polynomial Functions
Quadratic Functions
Graphing Techniques
Completing the Square
The Vertex Formula
Quadratic Models
Concept Preview
Concept Preview
3.2 Synthetic Division
Synthetic Division
Remainder Theorem
Potential Zeros of Polynomial Functions
Concept Preview
3.3 Zeros of Polynomial Functions
Factor Theorem
Rational Zeros Theorem
Proof
Number of Zeros
Conjugate Zeros Theorem
Proof
Zeros of a Polynomial Function
Descartes’ Rule of Signs
Concept Preview
3.4 Polynomial Functions: Graphs, Applications, and Models
Graphs of f(x)=axn
Graphs of General Polynomial Functions
Behavior at Zeros
Turning Points and End Behavior
Graphing Techniques
Intermediate Value and Boundedness Theorems
Proof
Approximations of Real Zeros
Polynomial Models
Concept Preview
3.5 Rational Functions: Graphs, Applications, and Models
The Reciprocal Function f(x)=1x
The Function f(x)=1×2
Asymptotes
Graphing Techniques
Rational Models
Concept Preview
3.6 Polynomial and Rational Inequalities
Polynomial Inequalities
Rational Inequalities
Concept Preview
Concept Preview
Concept Preview
3.7 Variation
Direct Variation
Inverse Variation
Combined and Joint Variation
Concept Preview
Concept Preview
Chapter 3 Test Prep
Key Terms
3.1
3.2
3.3
3.4
3.5
3.6
3.7
New Symbols
Quick Review
Chapter 3 Review Exercises
Chapter 3 Test
4 Inverse, Exponential, and Logarithmic Functions
4.1 Inverse Functions
One-to-One Functions
Inverse Functions
Equations of Inverses
An Application of Inverse Functions to Cryptography
Concept Preview
Concept Preview
4.2 Exponential Functions
Exponents and Properties
Exponential Functions
Exponential Equations
Compound Interest
The Number e and Continuous Compounding
Exponential Models
Concept Preview
Concept Preview
4.3 Logarithmic Functions
Logarithms
Logarithmic Equations
Logarithmic Functions
Properties of Logarithms
Proof
Concept Preview
Concept Preview
Concept Preview
Concept Preview
Concept Preview
4.4 Evaluating Logarithms and the Change-of-Base Theorem
Common Logarithms
Applications and Models with Common Logarithms
Natural Logarithms
Applications and Models with Natural Logarithms
Logarithms with Other Bases
Proof
Concept Preview
4.5 Exponential and Logarithmic Equations
Exponential Equations
Logarithmic Equations
Applications and Models
Concept Preview
Concept Preview
4.6 Applications and Models of Exponential Growth and Decay
The Exponential Growth or Decay Function
Growth Function Models
Decay Function Models
Concept Preview
Concept Preview
Chapter 4 Test Prep
Key Terms
4.1
4.2
4.3
4.4
4.6
New Symbols
Quick Review
Chapter 4 Review Exercises
Chapter 4 Test
5 Trigonometric Functions
5.1 Angles
Basic Terminology
Degree Measure
Standard Position
Coterminal Angles
Concept Preview
5.2 Trigonometric Functions
Trigonometric Functions
Quadrantal Angles
Reciprocal Identities
Signs and Ranges of Function Values
Pythagorean Identities
Quotient Identities
Concept Preview
Concept Preview
5.3 Trigonometric Function Values and Angle Measures
Right-Triangle-Based Definitions of the Trigonometric Functions
Cofunctions
Trigonometric Function Values of Special Angles
Reference Angles
Special Angles as Reference Angles
Determination of Angle Measures with Special Reference Angles
Calculator Approximations of Trigonometric Function Values
Calculator Approximations of Angle Measures
An Application
Concept Preview
Concept Preview
5.4 Solutions and Applications of Right Triangles
Historical Background
Significant Digits
Solving Triangles
Angles of Elevation or Depression
Bearing
Further Applications
Concept Preview
Concept Preview
Chapter 5 Test Prep
Key Terms
5.1
5.2
5.3
5.4
New Symbols
Quick Review
Chapter 5 Review Exercises
Chapter 5 Test
6 The Circular Functions and Their Graphs
6.1 Radian Measure
Radian Measure
Conversions between Degrees and Radians
Arc Length on a Circle
Area of a Sector of a Circle
Concept Preview
Concept Preview
6.2 The Unit Circle and Circular Functions
Circular Functions
Values of the Circular Functions
Determining a Number with a Given Circular Function Value
Linear and Angular Speed
Concept Preview
Concept Preview
6.3 Graphs of the Sine and Cosine Functions
Periodic Functions
Graph of the Sine Function
Graph of the Cosine Function
Techniques for Graphing, Amplitude, and Period
Connecting Graphs with Equations
A Trigonometric Model
Concept Preview
6.4 Translations of the Graphs of the Sine and Cosine Functions
Horizontal Translations
Vertical Translations
Combinations of Translations
A Trigonometric Model
Concept Preview
6.5 Graphs of the Tangent and Cotangent Functions
Graph of the Tangent Function
Graph of the Cotangent Function
Techniques for Graphing
Connecting Graphs with Equations
Concept Preview
6.6 Graphs of the Secant and Cosecant Functions
Graph of the Secant Function
Graph of the Cosecant Function
Techniques for Graphing
Connecting Graphs with Equations
Addition of Ordinates
Concept Preview
6.7 Harmonic Motion
Simple Harmonic Motion
Damped Oscillatory Motion
Concept Preview
Chapter 6 Test Prep
Key Terms
6.1
6.2
6.3
6.4
6.5
6.6
6.7
Quick Review
Chapter 6 Review Exercises
Chapter 6 Test
7 Trigonometric Identities and Equations
7.1 Fundamental Identities
Fundamental Identities
Uses of the Fundamental Identities
Concept Preview
Concept Preview
7.2 Verifying Trigonometric Identities
Strategies
Verifying Identities by Working with One Side
Verifying Identities by Working with Both Sides
Concept Preview
Concept Preview
7.3 Sum and Difference Identities
Cosine Sum and Difference Identities
Cofunction Identities
Sine and Tangent Sum and Difference Identities
Applications of the Sum and Difference Identities
Verifying an Identity
Concept Preview
Concept Preview
7.4 Double-Angle and Half-Angle Identities
Double-Angle Identities
An Application
Product-to-Sum and Sum-to-Product Identities
Half-Angle Identities
Verifying an Identity
Concept Preview
Concept Preview
7.5 Inverse Circular Functions
Review of Inverse Functions
Inverse Sine Function
Inverse Cosine Function
Inverse Tangent Function
Other Inverse Circular Functions
Inverse Function Values
Concept Preview
Concept Preview
7.6 Trigonometric Equations
Linear Methods
Zero-Factor Property Method
Quadratic Methods
Trigonometric Identity Substitutions
Equations with Half-Angles
Equations with Multiple Angles
Applications
Concept Preview
Concept Preview
Concept Preview
7.7 Equations Involving Inverse Trigonometric Functions
Solution for x in Terms of y Using Inverse Functions
Solution of Inverse Trigonometric Equations
Concept Preview
Chapter 7 Test Prep
New Symbols
Quick Review
Chapter 7 Review Exercises
Chapter 7 Test
8 Applications of Trigonometry
8.1 The Law of Sines
Congruency and Oblique Triangles
Derivation of the Law of Sines
Using the Law of Sines
Description of the Ambiguous Case
Area of a Triangle
Concept Preview
Concept Preview
Concept Preview
Concept Check
8.2 The Law of Cosines
Derivation of the Law of Cosines
Using the Law of Cosines
Heron’s Formula for the Area of a Triangle
Derivation of Heron’s Formula
Concept Preview
8.3 Geometrically Defined Vectors and Applications
Basic Terminology
The Equilibrant
Incline Applications
Navigation Applications
Concept Preview
Concept Preview
8.4 Algebraically Defined Vectors and the Dot Product
Algebraic Interpretation of Vectors
Operations with Vectors
The Dot Product and the Angle between Vectors
Concept Preview
8.5 Trigonometric (Polar) Form of Complex Numbers; Products and Quotients
The Complex Plane and Vector Representation
Trigonometric (Polar) Form
Converting between Rectangular and Trigonometric Forms
An Application of Complex Numbers to Fractals
Products of Complex Numbers in Trigonometric Form
Quotients of Complex Numbers in Trigonometric Form
Concept Preview
Concept Preview
8.6 De Moivre’s Theorem; Powers and Roots of Complex Numbers
Powers of Complex Numbers (De Moivre’s Theorem)
Roots of Complex Numbers
Concept Preview
Concept Preview
8.7 Polar Equations and Graphs
Polar Coordinate System
Graphs of Polar Equations
Conversion from Polar to Rectangular Equations
Classification of Polar Equations
Concept Preview
Concept Preview
Concept Preview
8.8 Parametric Equations, Graphs, and Applications
Basic Concepts
Parametric Graphs and Their Rectangular Equivalents
The Cycloid
Applications of Parametric Equations
Concept Preview
Concept Preview
Chapter 8 Test Prep
Key Terms
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
New Symbols
Quick Review
Chapter 8 Review Exercises
Chapter 8 Test
9 Systems and Matrices
9.1 Systems of Linear Equations
Linear Systems
Substitution Method
Elimination Method
Special Systems
Application of Systems of Equations
Linear Systems with Three Unknowns (Variables)
Application of Systems to Model Data
Concept Preview
9.2 Matrix Solution of Linear Systems
The Gauss-Jordan Method
Special Systems
The Gaussian Elimination Method
Concept Preview
9.3 Determinant Solution of Linear Systems
Determinants
Cofactors
n×n Determinants
Determinant Theorems
Cramer’s Rule
Concept Preview
9.4 Partial Fractions
Decomposition of Rational Expressions
Distinct Linear Factors
Repeated Linear Factors
Distinct Linear and Quadratic Factors
Repeated Quadratic Factors
Concept Preview
9.5 Nonlinear Systems of Equations
Nonlinear Systems with Real Solutions
Nonlinear Systems with Nonreal Complex Solutions
An Application of Nonlinear Systems
Concept Preview
9.6 Systems of Inequalities and Linear Programming
Linear Inequalities in Two Variables
Nonlinear Inequalities in Two Variables
Systems of Inequalities
Linear Programming
Concept Preview
Concept Preview
9.7 Properties of Matrices
Basic Definitions
Matrix Addition
Special Matrices
Matrix Subtraction
Scalar Multiplication
Matrix Multiplication
An Application of Matrix Algebra
Concept Preview
9.8 Matrix Inverses
Identity Matrices
Multiplicative Inverses
Solution of Systems Using Inverse Matrices
Concept Preview
Chapter 9 Test Prep
Key Terms
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
New Symbols
Quick Review
Chapter 9 Review Exercises
Chapter 9 Test
10 Analytic Geometry
10.1 Parabolas
Conic Sections
Horizontal Parabolas
Geometric Definition and Equations of Parabolas
An Application of Parabolas
10.2 Ellipses
Equations and Graphs of Ellipses
Translated Ellipses
Eccentricity
Applications of Ellipses
Chapter 10 Quiz (Sections 10.1–10.2)
10.3 Hyperbolas
Equations and Graphs of Hyperbolas
Translated Hyperbolas
Eccentricity
Concept Preview
Concept Preview
10.4 Summary of the Conic Sections
Characteristics
Identifying Conic Sections
Geometric Definition of Conic Sections
Chapter 10 Test Prep
Key Terms
10.1
10.2
10.3
New Symbols
Quick Review
Chapter 10 Review Exercises
Chapter 10 Test
11 Further Topics in Algebra
11.1 Sequences and Series
Sequences
Series and Summation Notation
Summation Properties and Rules
Concept Preview
Concept Preview
11.2 Arithmetic Sequences and Series
Arithmetic Sequences
Arithmetic Series
Concept Preview
Concept Preview
Concept Preview
11.3 Geometric Sequences and Series
Geometric Sequences
Geometric Series
Infinite Geometric Series
Annuities
Concept Preview
Concept Preview
11.4 The Binomial Theorem
A Binomial Expansion Pattern
Pascal’s Triangle
n-Factorial
Binomial Coefficients
The Binomial Theorem
kth Term of a Binomial Expansion
Concept Preview
11.5 Mathematical Induction
Principle of Mathematical Induction
Proofs of Statements
Generalized Principle of Mathematical Induction
Proof of the Binomial Theorem
Concept Preview
11.6 Basics of Counting Theory
Fundamental Principle of Counting
Permutations
Combinations
Characteristics That Distinguish Permutations from Combinations
Concept Preview
11.7 Basics of Probability
Basic Concepts
Complements and Venn Diagrams
Odds
Compound Events
Binomial Probability
Concept Preview
Chapter 11 Test Prep
Key Terms
11.1
11.2
11.3
11.4
11.6
11.7
New Symbols
Quick Review
Chapter 11 Review Exercises
Chapter 11 Test
Appendices
A Polar Form of Conic Sections
Equations and Graphs
Conversion from Polar to Rectangular Form
B Rotation of Axes
Derivation of Rotation Equations
Application of a Rotation Equation
C Geometry Formulas
Answers to Selected Exercises
To The Student
Chapter R Review of Basic Concepts
R.1 Exercises
R.2 Exercises
R.3 Exercises
R.4 Exercises
R.5 Exercises
R.6 Exercises
R.7 Exercises
R.8 Exercises
Chapter R Review Exercises
Chapter R Test
Chapter 1 Equations and Inequalities
1.1 Exercises
1.2 Exercises
1.3 Exercises
1.4 Exercises
Chapter 1 Quiz
1.5 Exercises
1.6 Exercises
Summary Exercises on Solving Equations
1.7 Exercises
1.8 Exercises
Chapter 1 Review Exercises
Chapter 1 Test
Chapter 2 Graphs and Functions
2.1 Exercises
2.2 Exercises
2.3 Exercises
2.4 Exercises
Chapter 2 Quiz
2.5 Exercises
Summary Exercises on Graphs, Circles, Functions, and Equations
2.6 Exercises
2.7 Exercises
Chapter 2 Quiz
2.8 Exercises
Chapter 2 Review Exercises
Chapter 2 Test
Chapter 3 Polynomial and Rational Functions
3.1 Exercises
3.2 Exercises
3.3 Exercises
3.4 Exercises
Summary Exercises on Polynomial Functions, Zeros, and Graphs
3.5 Exercises
Chapter 3 Quiz
3.6 Exercises
Summary Exercises on Solving Equations and Inequalities
3.7 Exercises
Chapter 3 Review Exercises
Chapter 3 Test
Chapter 4 Inverse, Exponential, and Logarithmic Functions
4.1 Exercises
4.2 Exercises
4.3 Exercises
Summary Exercises on Inverse, Exponential, and Logarithmic Functions
4.4 Exercises
Chapter 4 Quiz
4.5 Exercises
4.6 Exercises
Summary Exercises on Functions: Domains and Defining Equations
Chapter 4 Review Exercises
Chapter 4 Test
Chapter 5 Trigonometric Functions
5.1 Exercises
5.2 Exercises
5.3 Exercises
Chapter 5 Quiz
5.4 Exercises
Chapter 5 Review Exercises
Chapter 5 Test
Chapter 6 The Circular Functions and Their Graphs
6.1 Exercises
6.2 Exercises
6.3 Exercises
6.4 Exercises
Chapter 6 Quiz
6.5 Exercises
6.6 Exercises
Summary Exercises on Graphing Circular Functions
6.7 Exercises
Chapter 6 Review Exercises
Chapter 6 Test
Chapter 7 Trigonometric Identities and Equations
7.1 Exercises
7.2 Exercises
7.3 Exercises
Chapter 7 Quiz
7.4 Exercises
7.5 Exercises
7.6 Exercises
Chapter 7 Quiz
7.7 Exercises
Chapter 7 Review Exercises
Chapter 7 Test
Chapter 8 Applications of Trigonometry
8.1 Exercises
8.2 Exercises
Chapter 8 Quiz
8.3 Exercises
8.4 Exercises
Summary Exercises on Applications of Trigonometry and Vectors
8.5 Exercises
8.6 Exercises
Chapter 8 Quiz
8.7 Exercises
8.8 Exercises
Chapter 8 Review Exercises
Chapter 8 Test
Chapter 9 Systems and Matrices
9.1 Exercises
9.2 Exercises
9.3 Exercises
9.4 Exercises
Chapter 9 Quiz
9.5 Exercises
Summary Exercises on Systems of Equations
9.6 Exercises
9.7 Exercises
9.8 Exercises
Chapter 9 Review Exercises
Chapter 9 Test
Chapter 10 Analytic Geometry
10.1 Exercises
10.2 Exercises
Chapter 10 Quiz
10.3 Exercises
10.4 Exercises
Chapter 10 Review Exercises
Chapter 10 Test
Chapter 11 Further Topics in Algebra
11.1 Exercises
11.2 Exercises
11.3 Exercises
Summary Exercises on Sequences and Series
11.4 Exercises
11.5 Exercises
Chapter 11 Quiz
11.6 Exercises
11.7 Exercises
Chapter 11 Review Exercises
Chapter 11 Test
Appendices
Appendix A Exercises
Appendix B Exercises
Photo Credits
Index

Marge Lial (late) was always interested in math; it was her favorite subject in the first grade! Marge’s intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor’s and Master’s degrees from California State University at Sacramento, was affiliated with American River College. An avid reader and traveler, her travel experiences often found their way into her books as applications, exercise sets, and feature sets. Her interest in archeology led to trips to various digs and ruin sites, producing some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan.

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