Algebra and Trigonometry, Eleventh Edition
Michael Sullivan
Contents
Three Distinct Series xix
The Flagship Series xx
Preface to the Instructor xxi
Get the Most Out of MyLab Math xxvi
Resources for Success xxvii
Applications Index xxix
R Review 1
R.1 Real Numbers 2
Work with Sets • Classify Numbers • Evaluate Numerical Expressions
Work with Properties of Real Numbers
R.2 Algebra Essentials 17
Graph Inequalities • Find Distance on the Real Number Line • Evaluate
Algebraic
Expressions • Determine the Domain of a Variable • Use the
Laws of Exponents • Evaluate Square Roots • Use a Calculator to Evaluate
Exponents • Use Scientific Notation
R.3 Geometry Essentials 30
Use the Pythagorean Theorem and Its Converse • Know Geometry
Formulas
Understand Congruent Triangles and Similar Triangles
R.4 Polynomials 39
Recognize Monomials • Recognize Polynomials • Add and Subtract Polynomials
Multiply Polynomials • Know Formulas for Special Products • Divide
Polynomials
Using Long Division • Work with Polynomials in Two Variables
R.5 Factoring Polynomials 49
Factor the Difference of Two Squares and the Sum and Difference of Two
Cubes • Factor Perfect Squares • Factor a Second-Degree
Polynomial: x2 + Bx + C • Factor by Grouping • Factor a Second-Degree
Polynomial: Ax2 + Bx + C, A _ 1 • Complete the Square
R.6 Synthetic Division 57
Divide Polynomials Using Synthetic Division
R.7 Rational Expressions 61
Reduce a Rational Expression to Lowest Terms • Multiply and Divide
Rational
Expressions • Add and Subtract Rational Expressions • Use the
Least Common Multiple Method • Simplify Complex Rational Expressions
R.8 nth Roots; Rational Exponents 72
Work with nth Roots • Simplify Radicals • Rationalize Denominators
and Numerators • Simplify Expressions with Rational Exponents
1 Equations and Inequalities 81
1.1 Linear Equations 82
Solve a Linear Equation • Solve Equations That Lead to Linear Equations
Solve Problems That Can Be Modeled by Linear Equations
1.2 Quadratic Equations 92
Solve a Quadratic Equation by Factoring • Solve a Quadratic Equation Using
the Square Root Method • Solve a Quadratic Equation by Completing
the Square • Solve a Quadratic Equation Using the Quadratic Formula
Solve Problems That Can Be Modeled by Quadratic Equations
1.3 Complex Numbers; Quadratic Equations in the Complex
Number System 104
Add, Subtract, Multiply, and Divide Complex Numbers • Solve Quadratic
Equations in the Complex Number System
1.4 Radical Equations; Equations Quadratic in Form;
Factorable Equations 113
Solve Radical Equations • Solve Equations Quadratic in Form • Solve
Equations
by Factoring
1.5 Solving Inequalities 119
Use Interval Notation • Use Properties of Inequalities • Solve Inequalities
Solve Combined Inequalities
1.6 Equations and Inequalities Involving Absolute Value 130
Solve Equations Involving Absolute Value • Solve Inequalities Involving
Absolute Value
1.7 Problem Solving: Interest, Mixture, Uniform
Motion, Constant Rate Job Applications 134
Translate Verbal Descriptions into Mathematical Expressions • Solve
Interest
Problems • Solve Mixture Problems • Solve Uniform Motion
Problems
Solve Constant Rate Job Problems
Chapter Review 144
Chapter Test 147
Chapter Projects 147
x Contents
2 Graphs 149
2.1 The Distance and Midpoint Formulas 150
Use the Distance Formula • Use the Midpoint Formula
2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry 158
Graph Equations by Plotting Points • Find Intercepts from a Graph
Find Intercepts from an Equation • Test an Equation for Symmetry with
Respect to the x-Axis, the y-Axis, and the Origin • Know How to Graph Key
Equations
2.3 Lines 169
Calculate and Interpret the Slope of a Line • Graph Lines Given a Point
and the Slope • Find the Equation of a Vertical Line • Use the Point-Slope
Form of a Line; Identify Horizontal Lines • Use the Slope-Intercept Form of
a Line • Find an Equation of a Line Given Two Points • Graph Lines Written
in General Form Using Intercepts • Find Equations of Parallel Lines • Find
Equations of Perpendicular Lines
2.4 Circles 185
Write the Standard Form of the Equation of a Circle • Graph a Circle
Work with the General Form of the Equation of a Circle
2.5 Variation 191
Construct a Model Using Direct Variation • Construct a Model Using
Inverse
Variation • Construct a Model Using Joint Variation
Chapter Review 197
Chapter Test 200
Cumulative Review 200
Chapter Project 201
3 Functions and Their Graphs 202
3.1 Functions 203
Describe a Relation • Determine Whether a Relation Represents a Function
Use Function Notation; Find the Value of a Function • Find the Difference
Quotient of a Function • Find the Domain of a Function Defined by
an Equation • Form the Sum, Difference, Product, and Quotient of Two
Functions
3.2 The Graph of a Function 219
Identify the Graph of a Function • Obtain Information from or about the
Graph of a Function
3.3 Properties of Functions 229
Identify Even and Odd Functions from a Graph • Identify Even and
Odd Functions from an Equation • Use a Graph to Determine Where a
Function Is Increasing, Decreasing, or Constant • Use a Graph to Locate
Local
Maxima and Local Minima • Use a Graph to Locate the Absolute
Maximum and the Absolute Minimum • Use a Graphing Utility to
Approximate
Local Maxima and Local Minima and to Determine Where a
Function Is Increasing or Decreasing • Find the Average Rate of Change
of a Function
3.4 Library of Functions; Piecewise-defined Functions 242
Graph the Functions Listed in the Library of Functions • Analyze a
Piecewise-
defined Function
3.5 Graphing Techniques: Transformations 254
Graph Functions Using Vertical and Horizontal Shifts • Graph Functions
Using Compressions and Stretches • Graph Functions Using Reflections
about the x-Axis and the y-Axis
3.6 Mathematical Models: Building Functions 267
Build and Analyze Functions
Chapter Review 273
Chapter Test 277
Cumulative Review 278
Chapter Projects 278
4 Linear and Quadratic Functions 280
4.1 Properties of Linear Functions and Linear Models 281
Graph Linear Functions • Use Average Rate of Change to Identify Linear
Functions • Determine Whether a Linear Function Is Increasing, Decreasing,
or Constant • Build Linear Models from Verbal Descriptions
4.2 Building Linear Models from Data 291
Draw and Interpret Scatter Plots. • Distinguish between Linear and
Nonlinear
Relations • Use a Graphing Utility to Find the Line of Best Fit
4.3 Quadratic Functions and Their Properties 299
Graph a Quadratic Function Using Transformations • Identify the Vertex
and Axis of Symmetry of a Parabola • Graph a Quadratic Function Using
Its Vertex, Axis, and Intercepts • Find a Quadratic Function Given Its
Vertex and One Other Point • Find the Maximum or Minimum Value of a
Quadratic Function
4.4 Building Quadratic Models from Verbal Descriptions
and from Data 312
Build Quadratic Models from Verbal Descriptions • Build Quadratic Models
from Data
4.5 Inequalities Involving Quadratic Functions 321
Solve Inequalities Involving a Quadratic Function
Chapter Review 325
Chapter Test 327
Cumulative Review 328
Chapter Projects 329
5 Polynomial and Rational Functions 330
5.1 Polynomial Functions 331
Identify Polynomial Functions and Their Degree • Graph Polynomial
Functions
Using Transformations • Identify the Real Zeros of a Polynomial
Function and Their Multiplicity
5.2 Graphing Polynomial Functions; Models 346
Graph a Polynomial Function • Graph a Polynomial Function Using a
Graphing Utility • Build Cubic Models from Data
5.3 Properties of Rational Functions 354
Find the Domain of a Rational Function • Find the Vertical Asymptotes
of a Rational Function • Find a Horizontal or an Oblique Asymptote of a
Rational Function
5.4 The Graph of a Rational Function 365
Graph a Rational Function • Solve Applied Problems Involving
Rational Functions
5.5 Polynomial and Rational Inequalities 380
Solve Polynomial Inequalities • Solve Rational Inequalities
5.6 The Real Zeros of a Polynomial Function 387
Use the Remainder and Factor Theorems • Use Descartes’ Rule of Signs to
Determine the Number of Positive and the Number of Negative Real Zeros of
a Polynomial Function • Use the Rational Zeros Theorem to List the Potential
Rational Zeros of a Polynomial Function • Find the Real Zeros of a Polynomial
Function • Solve Polynomial Equations
Use the Theorem for Bounds on
Zeros • Use the Intermediate Value of Theorem
5.7 Complex Zeros; Fundamental Theorem of Algebra 401
Use the Conjugate Pairs Theorem • Find a Polynomial Function with
Specified
Zeros • Find the Complex Zeros of a Polynomial Function
Chapter Review 408
Chapter Test 411
Cumulative Review 412
Chapter Projects 413
6 Exponential and Logarithmic Functions 414
6.1 Composite Functions 415
Form a Composite Function • Find the Domain of a Composite Function
6.2 One-to-One Functions; Inverse Functions 423
Determine Whether a Function Is One-to-One • Obtain the Graph of the
Inverse
Function from the Graph of a One-to-One Function • Verify an
Inverse Function • Find the Inverse of a Function Defined by an Equation
6.3 Exponential Functions 435
Evaluate Exponential Functions • Graph Exponential Functions
Define the Number e • Solve Exponential Equations
6.4 Logarithmic Functions 452
Change Exponential Statements to Logarithmic Statements and Logarithmic
Statements to Exponential Statements • Evaluate Logarithmic Expressions
Determine the Domain of a Logarithmic Function • Graph Logarithmic
Functions • Solve Logarithmic Equations
6.5 Properties of Logarithms 465
Work with the Properties of Logarithms • Write a Logarithmic Expression
as a Sum or Difference of Logarithms • Write a Logarithmic Expression as a
Single Logarithm • Evaluate Logarithms Whose Base Is Neither 10 Nor e
6.6 Logarithmic and Exponential Equations 474
Solve Logarithmic Equations • Solve Exponential Equations • Solve
Logarithmic
and Exponential Equations Using a Graphing Utility
6.7 Financial Models 481
Determine the Future Value of a Lump Sum of Money • Calculate Effective
Rates of Return • Determine the Present Value of a Lump Sum of Money
Determine the Rate of Interest or the Time Required to Double a Lump
Sum of Money
6.8 Exponential Growth and Decay Models; Newton’s Law;
Logistic Growth and Decay Models 491
Model Populations That Obey the Law of Uninhibited Growth
Model Populations That Obey the Law of Uninhibited Decay
Use Newton’s Law of Cooling • Use Logistic Models
6.9 Building Exponential, Logarithmic, and Logistic
Models from Data 502
Build an Exponential Model from Data • Build a Logarithmic Model from
Data • Build a Logistic Model from Data
Chapter Review 509
Chapter Test 514
Cumulative Review 515
Chapter Projects 516
7 Trigonometric Functions 517
7.1 Angles, Arc Length, and Circular Motion 518
Angles and Degree Measure • Convert between Decimal and Degree,
Minute, Second Measures for Angles • Find the Length of an Arc of a Circle
Convert from Degrees to Radians and from Radians to Degrees • Find the
Area of a Sector of a Circle • Find the Linear Speed of an Object Traveling
in Circular Motion
7.2 Right Triangle Trigonometry 531
Find the Values of Trigonometric Functions of Acute Angles • Use
Fundamental
Identities • Find the Values of the Remaining Trigonometric
Functions, Given the Value of One of Them • Use the Complementary Angle
Theorem
7.3 Computing the Values of Trigonometric Functions
of Acute Angles 543
Find the Exact Values of the Trigonometric Functions of
p
4 = 45_ • Find
the Exact Values of the Trigonometric Functions of
p
6 = 30_ and
p
3 = 60_
Use a Calculator to Approximate the Values of the Trigonometric
Functions
of Acute Angles • Model and Solve Applied Problems Involving
Right Triangles
7.4 Trigonometric Functions of Any Angle 555
Find the Exact Values of the Trigonometric Functions for Any Angle • Use
Coterminal Angles to Find the Exact Value of a Trigonometric Function
Determine the Signs of the Trigonometric Functions of an Angle in a Given
Quadrant • Find the Reference Angle of an Angle • Use a Reference Angle
to Find the Exact Value of a Trigonometric Function • Find the Exact Values
of the Trigonometric Functions of an Angle, Given Information about the
Functions
7.5 Unit Circle Approach; Properties of the Trigonometric
Functions 566
Find the Exact Values of the Trigonometric Functions Using the Unit Circle
Know the Domain and Range of the Trigonometric Functions • Use
Periodic Properties to Find the Exact Values of the Trigonometric Functions
Use Even-Odd Properties to Find the Exact Values of the Trigonometric
Functions
7.6 Graphs of the Sine and Cosine Functions 579
Graph the Sine Function y = sin x and Functions of the Form y = A sin1vx2
Graph the Cosine Function y = cos x and Functions
of the Form
y = A cos1vx2 • Determine the Amplitude and Period of Sinusoidal
Functions
Graph Sinusoidal Functions Using Key Points • Find an
Equation
for a Sinusoidal Graph
7.7 Graphs of the Tangent, Cotangent, Cosecant,
and Secant Functions 594
Graph the Tangent Function y = tan x and the Cotangent Function y = cot x
Graph Functions of the Form y = A tan1vx2 + B and y = A cot1vx2 + B
Graph the Cosecant Function y = csc x and the Secant Function y = sec x
Graph Functions of the Form y = A csc1vx2 + B and y = A sec1vx2 + B
7.8 Phase Shift; Sinusoidal Curve Fitting 601
Graph Sinusoidal Functions of the Form y = A sin1vx – f2 + B
Build Sinusoidal Models from Data
Chapter Review 613
Chapter Test 618
Cumulative Review 619
Chapter Projects 620
8 Analytic Trigonometry 621
8.1 The Inverse Sine, Cosine, and Tangent Functions 622
Define the Inverse Sine Function • Find the Value of an Inverse Sine
Function
Define the Inverse Cosine Function • Find the Value of an
Inverse Cosine Function • Define the Inverse Tangent Function • Find the
Value of an Inverse Tangent Function • Use Properties of Inverse Functions
to Find Exact Values of Certain Composite Functions • Find the Inverse
Function of a Trigonometric Function • Solve Equations involving Inverse
Trigonometric Functions
8.2 The Inverse Trigonometric Functions (Continued) 635
Define the Inverse Secant, Cosecant, and Cotangent Functions • Find the
Value of Inverse Secant, Cosecant, and Cotangent Functions • Find the
Exact Value of Composite Functions Involving the Inverse Trigonometric
Functions • Write a Trigonometric Expression as an Algebraic Expression
8.3 Trigonometric Equations 641
Solve Equations Involving a Single Trigonometric Function • Solve
Trigonometric
Equations Using a Calculator • Solve Trigonometric Equations
Quadratic in Form • Solve Trigonometric Equations Using Fundamental
Identities • Solve Trigonometric Equations Using a Graphing Utility
8.4 Trigonometric Identities 651
Use Algebra to Simplify Trigonometric Expressions • Establish Identities
8.5 Sum and Difference Formulas 659
Use Sum and Difference Formulas to Find Exact Values • Use Sum and
Difference
Formulas to Establish Identities • Use Sum and Difference
Formulas Involving Inverse Trigonometric Functions • Solve Trigonometric
Equations Linear in Sine and Cosine
8.6 Double-angle and Half-angle Formulas 672
Use Double-angle Formulas to Find Exact Values • Use Double-angle Formulas
to Establish Identities • Use Half-angle Formulas to Find Exact Values
8.7 Product-to-Sum and Sum-to-Product Formulas 683
Express Products as Sums • Express Sums as Products
Chapter Review 687
Chapter Test 690
Cumulative Review 691
Chapter Projects 692
9 Applications of Trigonometric Functions 693
9.1 Applications Involving Right Triangles 694
Solve Right Triangles • Solve Applied Problems
9.2 The Law of Sines 700
Solve SAA or ASA Triangles • Solve SSA Triangles • Solve Applied Problems
9.3 The Law of Cosines 711
Solve SAS Triangles • Solve SSS Triangles • Solve Applied Problems
9.4 Area of a Triangle 718
Find the Area of SAS Triangles • Find the Area of SSS Triangles
9.5 Simple Harmonic Motion; Damped Motion; Combining Waves 724
Build a Model for an Object in Simple Harmonic Motion • Analyze
Simple Harmonic Motion • Analyze an Object in Damped Motion
Graph the Sum of Two Functions
Chapter Review 734
Chapter Test 736
Cumulative Review 737
Chapter Projects 737
10 Polar Coordinates; Vectors 739
10.1 Polar Coordinates 740
Plot Points Using Polar Coordinates • Convert from Polar Coordinates to
Rectangular Coordinates • Convert from Rectangular Coordinates to Polar
Coordinates • Transform Equations between Polar and Rectangular Forms
10.2 Polar Equations and Graphs 749
Identify and Graph Polar Equations by Converting to Rectangular Equations
Test Polar Equations for Symmetry • Graph Polar Equations by Plotting Points
10.3 The Complex Plane; De Moivre’s Theorem 764
Plot Points in the Complex Plane • Convert a Complex Number between
Rectangular Form and Polar Form or Exponential Form • Find Products
and Quotients of Complex Numbers • Use De Moivre’s Theorem • Find
Complex Roots
10.4 Vectors 773
Graph Vectors • Find a Position Vector • Add and Subtract Vectors
Algebraically
Find a Scalar Multiple and the Magnitude of a Vector
Find a Unit Vector • Find a Vector from Its Direction and Magnitude
Model with Vectors
10.5 The Dot Product 788
Find the Dot Product of Two Vectors • Find the Angle between Two Vectors
Determine Whether Two Vectors Are Parallel • Determine Whether Two
Vectors Are Orthogonal • Decompose a Vector into Two Orthogonal Vectors
Compute Work
Chapter Review 795
Chapter Test 798
Cumulative Review 799
Chapter Projects 799
11 Analytic Geometry 800
11.1 Conics 801
Know the Names of the Conics
11.2 The Parabola 802
Analyze Parabolas with Vertex at the Origin • Analyze Parabolas with
Vertex
at 1h, k2 • Solve Applied Problems Involving Parabolas
11.3 The Ellipse 811
Analyze Ellipses with Center at the Origin • Analyze Ellipses with
Center at 1h, k2 • Solve Applied Problems Involving Ellipses
11.4 The Hyperbola 821
Analyze Hyperbolas with Center at the Origin • Find the Asymptotes of
a Hyperbola • Analyze Hyperbolas with Center at (h, k) • Solve Applied
Problems Involving Hyperbolas
11.5 Rotation of Axes; General Form of a Conic 834
Identify a Conic • Use a Rotation of Axes to Transform Equations • Analyze
an Equation Using a Rotation of Axes • Identify Conics without Rotating
the Axes
11.6 Polar Equations of Conics 842
Analyze and Graph Polar Equations of Conics • Convert the Polar Equation
of a Conic to a Rectangular Equation
11.7 Plane Curves and Parametric Equations 849
Graph Parametric Equations • Find a Rectangular Equation for a Plane
Curve Defined Parametrically • Use Time as a Parameter in Parametric
Equations • Find Parametric Equations for Plane Curves Defined by
Rectangular
Equations
Chapter Review 862
Chapter Test 864
Cumulative Review 865
Chapter Projects 865
12 Systems of Equations and Inequalities 867
12.1 Systems of Linear Equations: Substitution and Elimination 868
Solve Systems of Equations by Substitution • Solve Systems of Equations
by Elimination • Identify Inconsistent Systems of Equations Containing
Two Variables • Express the Solution of a System of Dependent Equations
Containing Two Variables • Solve Systems of Three Equations Containing
Three Variables • Identify Inconsistent Systems of Equations Containing
Three Variables • Express the Solution of a System of Dependent Equations
Containing Three Variables
12.2 Systems of Linear Equations: Matrices 882
Write the Augmented Matrix of a System of Linear Equations • Write the
System of Equations from the Augmented Matrix • Perform Row Operations
on a Matrix • Solve a System of Linear Equations Using Matrices
12.3 Systems of Linear Equations: Determinants 896
Evaluate 2 by 2 Determinants • Use Cramer’s Rule to Solve a System of
Two Equations Containing Two Variables • Evaluate 3 by 3 Determinants
Use Cramer’s Rule to Solve a System of Three Equations Containing Three
Variables • Know Properties of Determinants
12.4 Matrix Algebra 907
Find the Sum and Difference of Two Matrices • Find Scalar Multiples of a
Matrix • Find the Product of Two Matrices • Find the Inverse of a Matrix
Solve a System of Linear Equations Using an Inverse Matrix
12.5 Partial Fraction Decomposition 924
Where Q Has Only Nonrepeated Linear Factors
Where Q Has Repeated Linear Factors • Decompose
Where Q Has a Nonrepeated Irreducible Quadratic Factor • Decompose
Where Q Has a Repeated Irreducible Quadratic Factor
12.6 Systems of Nonlinear Equations 933
Solve a System of Nonlinear Equations Using Substitution • Solve a
System of Nonlinear Equations Using Elimination
12.7 Systems of Inequalities 942
Graph an Inequality • Graph a System of Inequalities
12.8 Linear Programming 949
Set Up a Linear Programming Problem • Solve a Linear Programming
Problem
Chapter Review 957
Chapter Test 960
Cumulative Review 961
Chapter Projects 962
13 Sequences; Induction; the Binomial Theorem 963
13.1 Sequences 964
List the First Several Terms of a Sequence • List the Terms of a Sequence
Defined by a Recursive Formula • Use Summation Notation • Find the Sum
of a Sequence
13.2 Arithmetic Sequences 974
Determine Whether a Sequence Is Arithmetic • Find a Formula for an
Arithmetic
Sequence • Find the Sum of an Arithmetic Sequence
13.3 Geometric Sequences; Geometric Series 981
Determine Whether a Sequence Is Geometric • Find a Formula for a
Geometric
Sequence • Find the Sum of a Geometric Sequence
Determine Whether a Geometric Series Converges or Diverges
Solve Annuity Problems
13.4 Mathematical Induction 993
Prove Statements Using Mathematical Induction
13.5 The Binomial Theorem 997
b • Use the Binomial Theorem
Chapter Review 1003
Chapter Test 1006
Cumulative Review 1006
Chapter Projects 1007
14 Counting and Probability 1008
14.1 Counting 1009
Find All the Subsets of a Set • Count the Number of Elements in a Set
Solve Counting Problems Using the Multiplication Principle
14.2 Permutations and Combinations 1014
Solve Counting Problems Using Permutations Involving n Distinct Objects
Solve Counting Problems Using Combinations • Solve Counting Problems
Using Permutations Involving n Nondistinct Objects
14.3 Probability 1023
Construct Probability Models • Compute Probabilities of Equally Likely
Outcomes • Find Probabilities of the Union of Two Events • Use the
Complement Rule to Find Probabilities
Chapter Review 1033
Chapter Test 1035
Cumulative Review 1036
Chapter Projects 1036
Appendix Graphing Utilities A1
A.1 The Viewing Rectangle A1
A.2 Using a Graphing Utility to Graph Equations A3
A.3 Using a Graphing Utility to Locate Intercepts and
Check for Symmetry A5
A.4 Using a Graphing Utility to Solve Equations A6
A.5 Square Screens A8
A.6 Using a Graphing Utility to Graph Inequalities A9
A.7 Using a Graphing Utility to Solve Systems of Linear Equations A9
A.8 Using a Graphing Utility to Graph a Polar Equation A11
A.9 Using a Graphing Utility to Graph Parametric Equations A11
Answers AN1
Photo Credits C1
Subject Index I1