# Algebra and Trigonometry – 2e – Downloadable Textbook

Algebra and Trigonometry 2eÂ provides a comprehensive exploration of mathematical principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course.

## Overview

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- Jay Abramson, Arizona State University
- Copyright Year:Â
- ISBN 13: 9781951693404
- Publisher:Â OpenStax
- Language: English

## About the Book

*Algebra and Trigonometry 2e*Â 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.Â *Algebra and Trigonometry*Â *2e*Â offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what theyâ€™ve learned.

TheÂ *Algebra and Trigonometry 2e*Â revision focused onÂ 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 studentsâ€™ lives and interests.Â 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. The first edition ofÂ *Algebra and Trigonometry*Â by OpenStax is available in web viewÂ here.

## Table of Contents

- Preface
- Chapter 1. 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
- Exercises

- Chapter 2. 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
- Exercises

- 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
- Exercises

- Chapter 4. Linear Functions
- Introduction to Linear Functions
- 4.1. Linear Functions
- 4.2. Modeling with Linear Functionos
- 4.3. Fitting Linear Models to Data
- Chapter Review
- Exercises

- 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
- Exercises

- Chapter 6. Exponential and Logarithmic Functions
- Introduction to Exponential and Logarithmic Functions
- 6.1.Â Exponential Functions
- 6.2.Â Graphs of Exponential Functions
- 6.3.Â Logarithmic Functions
- 6.4.Â Graphs of Logarithmic Functions
- 6.5.Â Logarithmic Properties
- 6.6.Â Exponential and Logarithmic Equations
- 6.7.Â Exponential and Logarithmic Models
- 6.8.Â Fitting Exponential Models to Data
- Chapter Review
- Exercises

- ChapterÂ 7.Â The Unit Circle: Sine and Cosine Functions
- Introduction to The Unit Circle: Sine and Cosine Functions
- 7.1.Â Angles
- 7.2.Â Right Triangle Trigonometry
- 7.3.Â Unit Circle
- 7.4.Â The Other Trigonometric Functions
- Chapter Review
- Exercises

- Chapter 8. Periodic Functions
- Introduction to Periodic Functions
- 8.1Â Graphs of the Sine and Cosine Functions
- 8.2Â Graphs of the Other Trigonometric Functions
- 8.3Â Inverse Trigonometric Functions
- Chapter Review
- Exercises

- Chapter 9. Trigonometric Identities and Equations
- Introduction to Trigonometric Identities and Equations
- 9.1Â Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions
- 9.2Â Sum and Difference Identities
- 9.3Â Double-Angle, Half-Angle, and Reduction Formulas
- 9.4Â Sum-to-Product and Product-to-Sum Formulas
- 9.5Â Solving Trigonometric Equations
- Chapter Review
- Exercises

- Chapter 10. Further Applications of Trigonometry
- Introduction to Further Applications of Trigonometry
- 10.1Â Non-right Triangles: Law of Sines
- 10.2Â Non-right Triangles: Law of Cosines
- 10.3Â Polar Coordinates
- 10.4Â Polar Coordinates: Graphs
- 10.5Â Polar Form of Complex Numbers
- 10.6Â Parametric Equations
- 10.7Â Parametric Equations: Graphs
- 10.8Â Vectors
- Chapter Review
- Exercises

- Chapter 11. Systems of Equations and Inequalities
- Introduction to Systems of Equations and Inequalities
- 11.1Â Systems of Linear Equations: Two Variables
- 11.2Â Systems of Linear Equations: Three Variables
- 11.3Â Systems of Nonlinear Equations and Inequalities: Two Variables
- 11.4Â Partial Fractions
- 11.5Â Matrices and Matrix Operations
- 11.6Â Solving Systems with Gaussian Elimination
- 11.7Â Solving Systems with Inverses
- 11.8Â Solving Systems with Cramer’s Rule
- Chapter Review
- Exercises

- Chapter 12. Analytic Geometry
- Introduction to Analytic Geometry
- 12.1Â The Ellipse
- 12.2Â The Hyperbola
- 12.3Â The Parabola
- 12.4Â Rotation of Axes
- 12.5Â Conic Sections in Polar Coordinates
- Chapter Review
- Exercises

- Chapter 13. Sequences, Probability, and Counting Theory
- Introduction to Sequences, Probability, and Counting Theory
- 13.1Â Sequences and Their Notations
- 13.2Â Arithmetic Sequences
- 13.3Â Geometric Sequences
- 13.4Â Series and Their Notations
- 13.5Â Counting Principles
- 13.6Â Binomial Theorem
- 13.7Â Probability
- Chapter Review
- Exercises

- Appendix A. Proofs, Identities, and Toolkit Functions
- Answer Key
- Index

## Ancillary Material

## About the Contributors

### Author

Jay Abramson has been teaching Precalculus for over 35 years, the last 20 at Arizona State University, where he is a principal lecturer in the School of Mathematics and Statistics. His accomplishments at ASU include co-developing the universityâ€™s first hybrid and online math courses as well as an extensive library of video lectures and tutorials. In addition, he has served as a contributing author for two of Pearson Educationâ€™s math programs, NovaNet Precalculus and Trigonometry. Prior to coming to ASU, Jay taught at Texas State Technical College and Amarillo College. He received Teacher of the Year awards at both institutions.

Source: https://open.umn.edu/opentextbooks/textbooks/algebra-and-trigonometry