Algebra and Trigonometry (2nd edition)

Algebra and Trigonometry 2e provides a comprehensive exploration of mathematical principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensure that the book addresses the needs of a variety of courses. Algebra and Trigonometry 2e offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.

The Algebra and Trigonometry 2e revision focused on improving relevance and representation as well as mathematical clarity and accuracy. Introductory narratives, examples, and problems were reviewed and revised using a diversity, equity, and inclusion framework. Many contexts, scenarios, and images have been changed to become even more relevant to students’ lives and interests. To maintain our commitment to accuracy and precision, examples, exercises, and solutions were reviewed by multiple faculty experts. All improvement suggestions and errata updates from the first edition were considered and unified across the different formats of the text.

Senior Contributing Authors

Jay Abramson, Arizona State University


Contributing Authors

Valeree Falduto, Palm Beach State College
Rachael Gross, Towson University
David Lippman, Pierce College
Melonie Rasmussen, Pierce College
Rick Norwood, East Tennessee State University
Nicholas Belloit, Florida State College at Jacksonville
Harold Whipple, Formerly of Columbia College
Jean-Marie Magnier, Springfield Technical Community College
Christina Fernandez

Chapter 1 Prerequisites
• Introduction to Prerequisites
• 1.1 Real Numbers: Algebra Essentials
• 1.2 Exponents and Scientific Notation
• 1.3 Radicals and Rational Exponents
• 1.4 Polynomials
• 1.5 Factoring Polynomials
• 1.6 Rational Expressions
Chapter Review
o Key Terms
o Key Equations
o Key Concepts
Exercises
o Review Exercises
o Practice Test

Chapter 2 Equations and Inequalities
• Introduction to Equations and Inequalities
• 2.1 The Rectangular Coordinate Systems and Graphs
• 2.2 Linear Equations in One Variable
• 2.3 Models and Applications
• 2.4 Complex Numbers
• 2.5 Quadratic Equations
• 2.6 Other Types of Equations
• 2.7 Linear Inequalities and Absolute Value Inequalities
Chapter Review
o Key Terms
o Key Equations
o Key Concepts
Exercises
o Review Exercises
o Practice Test

Chapter 3 Functions
• Introduction to Functions
• 3.1 Functions and Function Notation
• 3.2 Domain and Range
• 3.3 Rates of Change and Behavior of Graphs
• 3.4 Composition of Functions
• 3.5 Transformation of Functions
• 3.6 Absolute Value Functions
• 3.7 Inverse Functions
Chapter Review
o Key Terms
o Key Equations
o Key Concepts
Exercises
o Review Exercises
o Practice Test

Chapter 4 Linear Functions
• Introduction to Linear Functions
• 4.1 Linear Functions
• 4.2 Modeling with Linear Functions
• 4.3 Fitting Linear Models to Data
Chapter Review
o Key Terms
o Key Concepts
Exercises
o Review Exercises
o Practice Test

Chapter 5 Polynomial and Rational Functions
• Introduction to Polynomial and Rational Functions
• 5.1 Quadratic Functions
• 5.2 Power Functions and Polynomial Functions
• 5.3 Graphs of Polynomial Functions
• 5.4 Dividing Polynomials
• 5.5 Zeros of Polynomial Functions
• 5.6 Rational Functions
• 5.7 Inverses and Radical Functions
• 5.8 Modeling Using Variation
Chapter Review
o Key Terms
o Key Equations
o Key Concepts
Exercises
o Review Exercises
o Practice Test

Chapter 6 Exponential and Logarithmic Functions
• Introduction to Exponential and Logarithmic Functions
• 6.1 Exponential Functions
• 6.2 Graphs of Exponential Functions
• 6.3 Logarithmic Functions
• 6.4 Graphs of Logarithmic Functions
• 6.5 Logarithmic Properties
• 6.6 Exponential and Logarithmic Equations
• 6.7 Exponential and Logarithmic Models
• 6.8 Fitting Exponential Models to Data
Chapter Review
o Key Terms
o Key Equations
o Key Concepts
Exercises
o Review Exercises
o Practice Test

Chapter 7 The Unit Circle: Sine and Cosine Functions
• Introduction to The Unit Circle: Sine and Cosine Functions
• 7.1 Angles
• 7.2 Right Triangle Trigonometry
• 7.3 Unit Circle
• 7.4 The Other Trigonometric Functions
Chapter Review
o Key Terms
o Key Equations
o Key Concepts
Exercises
o Review Exercises
o Practice Test

Chapter 8 Periodic Functions
• Introduction to Periodic Functions
• 8.1 Graphs of the Sine and Cosine Functions
• 8.2 Graphs of the Other Trigonometric Functions
• 8.3 Inverse Trigonometric Functions
Chapter Review
o Key Terms
o Key Equations
o Key Concepts
Exercises
o Review Exercises
o Practice Test

Chapter 9 Trigonometric Identities and Equations
• Introduction to Trigonometric Identities and Equations
• 9.1 Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions
• 9.2 Sum and Difference Identities
• 9.3 Double-Angle, Half-Angle, and Reduction Formulas
• 9.4 Sum-to-Product and Product-to-Sum Formulas
• 9.5 Solving Trigonometric Equations
Chapter Review
o Key Terms
o Key Equations
o Key Concepts
Exercises
o Review Exercises
o Practice Test

Chapter 10 Further Applications of Trigonometry
• Introduction to Further Applications of Trigonometry
• 10.1 Non-right Triangles: Law of Sines
• 10.2 Non-right Triangles: Law of Cosines
• 10.3 Polar Coordinates
• 10.4 Polar Coordinates: Graphs
• 10.5 Polar Form of Complex Numbers
• 10.6 Parametric Equations
• 10.7 Parametric Equations: Graphs
• 10.8 Vectors
Chapter Review
o Key Terms
o Key Equations
o Key Concepts
Exercises
o Review Exercises
o Practice Test

Chapter 11 Systems of Equations and Inequalities
• Introduction to Systems of Equations and Inequalities
• 11.1 Systems of Linear Equations: Two Variables
• 11.2 Systems of Linear Equations: Three Variables
• 11.3 Systems of Nonlinear Equations and Inequalities: Two Variables
• 11.4 Partial Fractions
• 11.5 Matrices and Matrix Operations
• 11.6 Solving Systems with Gaussian Elimination
• 11.7 Solving Systems with Inverses
• 11.8 Solving Systems with Cramer's Rule
Chapter Review
o Key Terms
o Key Equations
o Key Concepts
Exercises
o Review Exercises
o Practice Test

Chapter 12 Analytic Geometry
• Introduction to Analytic Geometry
• 12.1 The Ellipse
• 12.2 The Hyperbola
• 12.3 The Parabola
• 12.4 Rotation of Axes
• 12.5 Conic Sections in Polar Coordinates
Chapter Review
o Key Terms
o Key Equations
o Key Concepts
Exercises
o Review Exercises
o Practice Test

Chapter 13 Sequences, Probability, and Counting Theory
• Introduction to Sequences, Probability and Counting Theory
• 13.1 Sequences and Their Notations
• 13.2 Arithmetic Sequences
• 13.3 Geometric Sequences
• 13.4 Series and Their Notations
• 13.5 Counting Principles
• 13.6 Binomial Theorem
• 13.7 Probability
Chapter Review
o Key Terms
o Key Equations
o Key Concepts
Exercises
o Review Exercises
o Practice Test