Textbook
Algebra and TrigonometryMarch 2011, ©2012

Axler Algebra & Trigonometry focuses on depth, not breadth of topics by exploring necessary topics in greater detail. Readers will benefit from the straightforward definitions and plentiful examples of complex concepts.
The Student Solutions Manual is integrated at the end of every section. The proximity of the solutions encourages students to go back and read the main text as they are working through the problems and exercises. The inclusion of the manual also saves students money.
Axler Algebra & Trigonometry is available with WileyPLUS; an innovative, researchbased, online environment for effective teaching and learning.
Preface to the Instructor
Acknowledgments
Preface to the Student
1 The Real Numbers
1.1 The Real Line
Construction of the Real Line
Is Every Real Number Rational?
Problems
1.2 Algebra of the Real Numbers
Commutativity and Associativity
The Order of Algebraic Operations
The Distributive Property
Additive Inverses and Subtraction
Multiplicative Inverses and the Algebra of Fractions
Symbolic Calculators
Exercises, Problems, and Workedout Solutions
1.3 Inequalities
Positive and Negative Numbers
Lesser and Greater
Intervals
Absolute Value
Exercises, Problems, and Workedout Solutions
Chapter Summary and Chapter Review Questions
2 Combining Algebra and Geometry
2.1 The Coordinate Plane
Coordinates
Graphs of Equations
Distance Between Two Points
Length, Perimeter, and Circumference
Exercises, Problems, and Workedout Solutions
2.2 Lines
Slope
The Equation of a Line
Parallel Lines
Perpendicular Lines
Midpoints
Exercises, Problems, and Workedout Solutions
2.3 Quadratic Expressions and Conic Sections
Completing the Square
The Quadratic Formula
Circles
Ellipses
Parabolas
Hyperbolas
Exercises, Problems, and Workedout Solutions
2.4 Area
Squares, Rectangles, and Parallelograms
Triangles and Trapezoids
Stretching
Circles and Ellipses
Exercises, Problems, and Workedout Solutions
Chapter Summary and Chapter Review Questions
3 Functions and Their Graphs
3.1 Functions
Definition and Examples
The Graph of a Function
The Domain of a Function
The Range of a Function
Functions via Tables
Exercises, Problems, and Workedout Solutions
3.2 Function Transformations and Graphs
Vertical Transformations: Shifting, Stretching, and Flipping
Horizontal Transformations: Shifting, Stretching, Flipping
Combinations of Vertical Function Transformations
Even Functions
Odd Functions
Exercises, Problems, and Workedout Solutions
3.3 Composition of Functions
Combining Two Functions
Definition of Composition
Order Matters in Composition
Decomposing Functions
Composing More than Two Functions
Function Transformations as Compositions
Exercises, Problems, and Workedout Solutions
3.4 Inverse Functions
The Inverse Problem
Onetoone Functions
The Definition of an Inverse Function
The Domain and Range of an Inverse Function
The Composition of a Function and Its Inverse
Comments about Notation
Exercises, Problems, and Workedout Solutions
3.5 A Graphical Approach to Inverse Functions
The Graph of an Inverse Function
Graphical Interpretation of OnetoOne
Increasing and Decreasing Functions
Inverse Functions via Tables
Exercises, Problems, and Workedout Solutions
Chapter Summary and Chapter Review Questions
4 Polynomial and Rational Functions
4.1 Integer Exponents
Positive Integer Exponents
Properties of Exponents
Defining x0
Negative Integer Exponents
Manipulations with Exponents
Exercises, Problems, and Workedout Solutions
4.2 Polynomials
The Degree of a Polynomial
The Algebra of Polynomials
Zeros and Factorization of Polynomials
The Behavior of a Polynomial Near _1
Graphs of Polynomials
Exercises, Problems, and Workedout Solutions
4.3 Rational Functions
Ratios of Polynomials
The Algebra of Rational Functions
Division of Polynomials
The Behavior of a Rational Function Near _1
Graphs of Rational Functions
Exercises, Problems, and Workedout Solutions
4.4 Complex Numbers
The Complex Number System
Arithmetic with Complex Numbers
Complex Conjugates and Division of Complex Numbers
Zeros and Factorization of Polynomials, Revisited
Exercises, Problems, and Workedout Solutions
Chapter Summary and Chapter Review Questions
5 Exponents and Logarithms
5.1 Exponents and Exponential Functions
Roots
Rational Exponents
Real Exponents
Exponential Functions
Exercises, Problems, and Workedout Solutions
5.2 Logarithms as Inverses of Exponential Functions
Logarithms Base 2
Logarithms with Any Base
Common Logarithms and the Number of Digits
Logarithm of a Power
Radioactive Decay and HalfLife
Exercises, Problems, and Workedout Solutions
5.3 Applications of Logarithms
Logarithm of a Product
Logarithm of a Quotient
Earthquakes and the Richter Scale
Sound Intensity and Decibels
Star Brightness and Apparent Magnitude
Change of Base
Exercises, Problems, and Workedout Solutions
5.4 Exponential Growth
Functions with Exponential Growth
Population Growth
Compound Interest
Exercises, Problems, and Workedout Solutions
Chapter Summary and Chapter Review Questions
6 e and the Natural Logarithm
6.1 Defining e and ln
Estimating Area Using Rectangles
Defining e
Defining the Natural Logarithm
Properties of the Exponential Function and ln
Exercises, Problems, and Workedout Solutions
6.2 Approximations with e and ln
Approximation of the Natural Logarithm
Inequalities with the Natural Logarithm
Approximations with the Exponential Function
An Area Formula
Exercises, Problems, and Workedout Solutions
6.3 Exponential Growth Revisited
Continuously Compounded Interest
Continuous Growth Rates
Doubling Your Money
Exercises, Problems, and Workedout Solutions
Chapter Summary and Chapter Review Questions
7 Trigonometric Functions
7.1 The Unit Circle
The Equation of the Unit Circle
Angles in the Unit Circle
Negative Angles
Angles Greater Than 360_
Length of a Circular Arc
Special Points on the Unit Circle
Exercises, Problems, and Workedout Solutions
7.2 Radians
A Natural Unit of Measurement for Angles
Negative Angles
Angles Greater Than 2_
Length of a Circular Arc
Area of a Slice
Special Points on the Unit Circle
Exercises, Problems, and Workedout Solutions
7.3 Cosine and Sine
Definition of Cosine and Sine
Cosine and Sine of Special Angles
The Signs of Cosine and Sine
The Key Equation Connecting Cosine and Sine
The Graphs of Cosine and Sine
Exercises, Problems, and Workedout Solutions
7.4 More Trigonometric Functions
Definition of Tangent
Tangent of Special Angles
The Sign of Tangent
Connections between Cosine, Sine, and Tangent
The Graph of Tangent
Three More Trigonometric Functions
Exercises, Problems, and Workedout Solutions
7.5 Trigonometry in Right Triangles
Trigonometric Functions via Right Triangles
Two Sides of a Right Triangle
One Side and One Angle of a Right Triangle
Exercises, Problems, and Workedout Solutions
7.6 Trigonometric Identities
The Relationship Between Cosine and Sine
Trigonometric Identities for the Negative of an Angle
Trigonometric Identities with
Trigonometric Identities Involving a Multiple of
Exercises, Problems, and Workedout Solutions
Chapter Summary and Chapter Review Questions
8 Trigonometric Algebra and Geometry
8.1 Inverse Trigonometric Functions
The Arccosine Function
The Arcsine Function
The Arctangent Function
Exercises, Problems, and Workedout Solutions
8.2 Inverse Trigonometric Identities
The Arccosine, Arcsine, and Arctangent of
t: Graphical
Approach
The Arccosine, Arcsine, and Arctangent of
t: Algebraic
Approach
Arccosine Plus Arcsine
The Arctangent of 1t
Composition of Trigonometric Functions and Their Inverses
More Compositions with Inverse Trigonometric Functions
Exercises, Problems, and Workedout Solutions
8.3 Using Trigonometry to Compute Area
The Area of a Triangle via Trigonometry
Ambiguous Angles
The Area of a Parallelogram via Trigonometry
The Area of a Polygon
Exercises, Problems, and Workedout Solutions
8.4 The Law of Sines and the Law of Cosines
The Law of Sines
Using the Law of Sines
The Law of Cosines
Using the Law of Cosines
When to Use Which Law
Exercises, Problems, and Workedout Solutions
8.5 DoubleAngle and HalfAngle Formulas
The Cosine of 2_
The Sine of 2_
The Tangent of 2_
The Cosine and Sine of _2
The Tangent of _2
Exercises, Problems, and Workedout Solutions
8.6 Addition and Subtraction Formulas
The Cosine of a Sum and Difference
The Sine of a Sum and Difference
The Tangent of a Sum and Difference
Exercises, Problems, and Workedout Solutions
Chapter Summary and Chapter Review Questions
9 Applications of Trigonometry
9.1 Parametric Curves
Curves in the Coordinate Plane
Graphing Inverse Functions as Parametric Curves
Shifting, Stretching, or Flipping a Parametric Curve
Exercises, Problems, and Workedout Solutions
9.2 Transformations of Trigonometric Functions
Amplitude
Period
Phase Shift
Exercises, Problems, and Workedout Solutions
9.3 Polar Coordinates
Defining Polar Coordinates
Converting from Polar to Rectangular Coordinates
Converting from Rectangular to Polar Coordinates
Graphs of Polar Equations
Exercises, Problems, and Workedout Solutions
9.4 Vectors
An Algebraic and Geometric Introduction to Vectors
Vector Addition
Vector Subtraction
The Dot Product
Exercises, Problems, and Workedout Solutions
9.5 The Complex Plane
Complex Numbers as Points in the Plane
Geometric Interpretation of Complex Multiplication and Division
De Moivre’s Theorem
Finding Complex Roots
Exercises, Problems, and Workedout Solutions
Chapter Summary and Chapter Review Questions
10 Systems of Equations and Inequalities
10.1 Equations and Systems of Equations
Solving an Equation
Solving a System of Equations
Systems of Linear Equations
Matrices
Exercises, Problems, and Workedout Solutions
10.2 Solving Systems of Linear Equations
Gaussian Elimination
Gaussian Elimination with Matrices
Special Cases—No Solutions
Special Cases—Infinitely Many Solutions
Exercises, Problems, and Workedout Solutions
10.3 Matrix Algebra
Adding and Subtracting Matrices
Multiplying Matrices
The Inverse of a Matrix
Exercises, Problems, and Workedout Solutions
Chapter Summary and Chapter Review Questions
11 Sequences, Series, and Limits
11.1 Sequences
Introduction to Sequences
Arithmetic Sequences
Geometric Sequences
RecursivelyDefined Sequences
Exercises, Problems, and Workedout Solutions
11.2 Series
Sums of Sequences
Arithmetic Series
Geometric Series
Summation Notation
The Binomial Theorem
Exercises, Problems, and Workedout Solutions
11.3 Limits
Introduction to Limits
Infinite Series
Decimals as Infinite Series
Special Infinite Series
Exercises, Problems, and Workedout Solutions
Chapter Summary and Chapter Review Questions
 Depth, Not Breadth: Topics have been carefully selected to get at the heart of algebraic weakness by narrowing down to key sets of skills which are regularly revisited from varied perspectives.
 Unitcircle Approach: This approach is used because calculus requires the unitcircle approach and it allows for a wellmotivated introduction to radian measure. Once the approach has been introduced, applications to right triangles are given.
 Exercises and Problems: The difference between an exercise and a problem is that each exercise has a unique correct answer that is a mathematical object such as a number or a function, while the solutions to problems consist of explanations or examples. The solutions to the oddnumbered exercises appear directly behind the relevant section.
 Variety: Exercises and problems in this book vary greatly in difficulty and purpose. Some exercises and problems are designed to hone algebraic manipulation skills; other exercises and problems are designed to push students to genuine understanding. Applications are written to reflect real scenarios, not artificial examples.
 Integrated Student's Solutions Manual: The solutions manual encourages students to read the main text and students will save money by not having to purchase a separate solutions manual.
 Designed to be Read: The writing style and layout are meant to induce students to read and understand the material. Explanations are more plentiful than typically found in College Algebra books, with examples of concepts making the ideas concrete whenever possible.
 Calculator Problems: A symbol appears next to problems that require a calculator, and some exercises and problems are designed to make students realize that by understanding the material, they can overcome the limitations of calculators.
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