Algebra and Trigonometry [4 ed.] 9781305071742

Table of contents :
Contents
Preface
To the Student
Are You Ready for This Course?
Prologue: Principles of Problem Solving
Ch P: Prerequisites
Section P.1: Modeling the Real World with Algebra
Section P.2: Real Numbers
Section P.3: Integer Exponents and Scientific Notation
Section P.4: Rational Exponents and Radicals
Section P.5: Algebraic Expressions
Section P.6: Factoring
Section P.7: Rational Expressions
Section P.8: Solving Basic Equations
Section P.9: Modeling with Equations
Chapter P Review
Chapter P Test
Focus on Modeling: Making the Best Decisions
Ch 1: Equations and Graphs
Section 1.1: The Coordinate Plane
Section 1.2: Graphs of Equations in Two Variables; Circles
Section 1.3: Lines
Section 1.4: Solving Quadratic Equations
Section 1.5: Complex Numbers
Section 1.6: Solving Other Types of Equations
Section 1.7: Solving Inequalities
Section 1.8: Solving Absolute Value Equations and Inequalities
Section 1.9: Solving Equations and Inequalities Graphically
Section 1.10: Modeling Variation
Chapter 1 Review
Chapter 1 Test
Focus on Modeling: Fitting Lines to Data
Ch 2: Functions
Section 2.1: Functions
Section 2.2: Graphs of Functions
Section 2.3: Getting Information from the Graph of a Function
Section 2.4: Average Rate of Change of a Function
Section 2.5: Linear Functions and Models
Section 2.6: Transformations of Functions
Section 2.7: Combining Functions
Section 2.8: One-to-One Functions and Their Inverses
Chapter 2 Review
Chapter 2 Test
Focus on Modeling: Modeling with Functions
Ch 3: Polynomial and Rational Functions
Section 3.1: Quadratic Functions and Models
Section 3.2: Polynomial Functions and Their Graphs
Section 3.3: Dividing Polynomials
Section 3.4: Real Zeros of Polynomials
Section 3.5: Complex Zeros and the Fundamental Theorem of Algebra
Section 3.6: Rational Functions
Section 3.7: Polynomial and Rational Inequalities
Chapter 3 Review
Chapter 3 Test
Focus on Modeling: Fitting Polynomial Curves to Data
Ch 4: Exponential and Logarithmic Functions
Section 4.1: Exponential Functions
Section 4.2: The Natural Exponential Function
Section 4.3: Logarithmic Functions
Section 4.4: Laws of Logarithms
Section 4.5: Exponential and Logarithmic Equations
Section 4.6: Modeling with Exponential Functions
Section 4.7: Logarithmic Scales
Chapter 4 Review
Chapter 4 Test
Focus on Modeling: Fitting Exponential and Power Curves to Data
Ch 5: Trigonometric Functions: Right Triangle Approach
Section 5.1: Angle Measure
Section 5.2: Trigonometry of Right Triangles
Section 5.3: Trigonometric Functions of Angles
Section 5.4: Inverse Trigonometric Functions and Right Triangles
Section 5.5: The Law of Sines
Section 5.6: The Law of Cosines
Chapter 5 Review
Chapter 5 Test
Focus on Modeling: Surveying
Ch 6: Trigonometric Functions: Unit Circle Approach
Section 6.1: The Unit Circle
Section 6.2: Trigonometric Functions of Real Numbers
Section 6.3: Trigonometric Graphs
Section 6.4: More Trigonometric Graphs
Section 6.5: Inverse Trigonometric Functions and Their Graphs
Section 6.6: Modeling Harmonic Motion
Chapter 6 Review
Chapter 6 Test
Focus on Modeling: Fitting Sinusoidal Curves to Data
Ch 7: Analytic Trigonometry
Section 7.1: Trigonometric Identities
Section 7.2: Addition and Subtraction Formulas
Section 7.3: Double-Angle, Half-Angle, and Product-Sum Formulas
Section 7.4: Basic Trigonometric Equations
Section 7.5: More Trigonometric Equations
Chapter 7 Review
Chapter 7 Test
Focus on Modeling: Traveling and Standing Waves
Ch 8: Polar Coordinates and Parametric Equations
Chapter Overview
Section 8.1: Polar Coordinates
Section 8.2: Graphs of Polar Equations
Section 8.3: Polar Form of Complex Numbers; De Moivre's Theorem
Section 8.4: Plane Curves and Parametric Equations
Chapter 8 Review
Chapter 8 Test
Focus on Modeling: The Path of a Projectile
Ch 9: Vectors in Two and Three Dimensions
Section 9.1: Vectors in Two Dimensions
Section 9.2: The Dot Product
Section 9.3: Three-Dimensional Coordinate Geometry
Section 9.4: Vectors in Three Dimensions
Section 9.5: The Cross Product
Section 9.6: Equations of Lines and Planes
Chapter 9 Review
Chapter 9 Test
Focus on Modeling: Vector Fields
Ch 10: Systems of Equations and Inequalities
Chapter Overview
Section 10.1: Systems of Linear Equations in Two Variables
Section 10.2: Systems of Linear Equations in Several Variables
Section 10.3: Partial Fractions
Section 10.4: Systems of Nonlinear Equations
Section 10.5: Systems of Inequalities
Chapter 10 Review
Chapter 10 Test
Focus on Modeling: Linear Programming
Ch 11: Matrices and Determinants
Section 11.1: Matrices and Systems of Linear Equations
Section 11.2: The Algebra of Matrices
Section 11.3: Inverses of Matrices and Matrix Equations
Section 11.4: Determinants and Cramer's Rule
Chapter 11 Review
Chapter 11 Test
Focus on Modeling: Computer Graphics
Ch 12: Conic Sections
Section 12.1: Parabolas
Section 12.2: Ellipses
Section 12.3: Hyperbolas
Section 12.4: Shifted Conics
Section 12.5: Rotation of Axes
Section 12.6: Polar Equations of Conics
Chapter 12 Review
Chapter 12 Test
Focus on Modeling: Conics in Architecture
Ch 13: Sequences and Series
Section 13.1: Sequences and Summation Notation
Section 13.2: Arithmetic Sequences
Section 13.3: Geometric Sequences
Section 13.4: Mathematics of Finance
Section 13.5: Mathematical Induction
Section 13.6: The Binomial Theorem
Chapter 13 Review
Chapter 13 Test
Focus on Modeling: Modeling with Recursive Sequences
Ch 14: Counting and Probability
Section 14.1: Counting
Section 14.2: Probability
Section 14.3: Binomial Probability
Section 14.4: Expected Value
Chapter 14 Review
Chapter 14 Test
Focus on Modeling: The Monte Carlo Method
Appendix A: Geometry Review
Appendix B: Calculations and Significant Figures
Appendix C: Graphing with a Graphing Calculator
Appendix D: Using the TI-83/84 Graphing Calculator
Answers
Index