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Algebra and Trigonometry 2e

by Jay Abramson

Published by OpenStax

MathematicsCollege

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. The first edition of Algebra and Trigonometry by OpenStax is available in web view here . If you have encountered a white screen while accessing your OpenStax textbook, our developers suggest closing all of your OpenStax.org tabs and then loading the book again.

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Attribution

Adapted from Algebra and Trigonometry 2e by Jay Abramson, published by OpenStax (Rice University) under CC BY-NC-SA 4.0 (https://creativecommons.org/licenses/by-nc-sa/4.0/). Access the original for free at https://openstax.org/details/books/algebra-and-trigonometry-2e. Changes: converted to CuraCourse lessons, with interactive practice added.

Table of contents

107 pages in 15 modules. Sign up to read and adopt them.

  1. Preface1 page
    1. Preface
  2. 1Prerequisites8 pages
    1. Introduction to Prerequisites
    2. 1.1Real Numbers: Algebra Essentials
    3. 1.2Exponents and Scientific Notation
    4. 1.3Radicals and Rational Exponents
    5. 1.4Polynomials
    6. 1.5Factoring Polynomials
    7. 1.6Rational Expressions
    8. Practice
  3. 2Equations and Inequalities9 pages
    1. Introduction to Equations and Inequalities
    2. 2.1The Rectangular Coordinate Systems and Graphs
    3. 2.2Linear Equations in One Variable
    4. 2.3Models and Applications
    5. 2.4Complex Numbers
    6. 2.5Quadratic Equations
    7. 2.6Other Types of Equations
    8. 2.7Linear Inequalities and Absolute Value Inequalities
    9. Practice
  4. 3Functions9 pages
    1. Introduction to Functions
    2. 3.1Functions and Function Notation
    3. 3.2Domain and Range
    4. 3.3Rates of Change and Behavior of Graphs
    5. 3.4Composition of Functions
    6. 3.5Transformation of Functions
    7. 3.6Absolute Value Functions
    8. 3.7Inverse Functions
    9. Practice
  5. 4Linear Functions5 pages
    1. Introduction to Linear Functions
    2. 4.1Linear Functions
    3. 4.2Modeling with Linear Functions
    4. 4.3Fitting Linear Models to Data
    5. Practice
  6. 5Polynomial and Rational Functions10 pages
    1. Introduction to Polynomial and Rational Functions
    2. 5.1Quadratic Functions
    3. 5.2Power Functions and Polynomial Functions
    4. 5.3Graphs of Polynomial Functions
    5. 5.4Dividing Polynomials
    6. 5.5Zeros of Polynomial Functions
    7. 5.6Rational Functions
    8. 5.7Inverses and Radical Functions
    9. 5.8Modeling Using Variation
    10. Practice
  7. 6Exponential and Logarithmic Functions10 pages
    1. Introduction to Exponential and Logarithmic Functions
    2. 6.1Exponential Functions
    3. 6.2Graphs of Exponential Functions
    4. 6.3Logarithmic Functions
    5. 6.4Graphs of Logarithmic Functions
    6. 6.5Logarithmic Properties
    7. 6.6Exponential and Logarithmic Equations
    8. 6.7Exponential and Logarithmic Models
    9. 6.8Fitting Exponential Models to Data
    10. Practice
  8. 7The Unit Circle: Sine and Cosine Functions6 pages
    1. Introduction to The Unit Circle: Sine and Cosine Functions
    2. 7.1Angles
    3. 7.2Right Triangle Trigonometry
    4. 7.3Unit Circle
    5. 7.4The Other Trigonometric Functions
    6. Practice
  9. 8Periodic Functions5 pages
    1. Introduction to Periodic Functions
    2. 8.1Graphs of the Sine and Cosine Functions
    3. 8.2Graphs of the Other Trigonometric Functions
    4. 8.3Inverse Trigonometric Functions
    5. Practice
  10. 9Trigonometric Identities and Equations7 pages
    1. Introduction to Trigonometric Identities and Equations
    2. 9.1Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions
    3. 9.2Sum and Difference Identities
    4. 9.3Double-Angle, Half-Angle, and Reduction Formulas
    5. 9.4Sum-to-Product and Product-to-Sum Formulas
    6. 9.5Solving Trigonometric Equations
    7. Practice
  11. 10Further Applications of Trigonometry10 pages
    1. Introduction to Further Applications of Trigonometry
    2. 10.1Non-right Triangles: Law of Sines
    3. 10.2Non-right Triangles: Law of Cosines
    4. 10.3Polar Coordinates
    5. 10.4Polar Coordinates: Graphs
    6. 10.5Polar Form of Complex Numbers
    7. 10.6Parametric Equations
    8. 10.7Parametric Equations: Graphs
    9. 10.8Vectors
    10. Practice
  12. 11Systems of Equations and Inequalities10 pages
    1. Introduction to Systems of Equations and Inequalities
    2. 11.1Systems of Linear Equations: Two Variables
    3. 11.2Systems of Linear Equations: Three Variables
    4. 11.3Systems of Nonlinear Equations and Inequalities: Two Variables
    5. 11.4Partial Fractions
    6. 11.5Matrices and Matrix Operations
    7. 11.6Solving Systems with Gaussian Elimination
    8. 11.7Solving Systems with Inverses
    9. 11.8Solving Systems with Cramer's Rule
    10. Practice
  13. 12Analytic Geometry7 pages
    1. Introduction to Analytic Geometry
    2. 12.1The Ellipse
    3. 12.2The Hyperbola
    4. 12.3The Parabola
    5. 12.4Rotation of Axes
    6. 12.5Conic Sections in Polar Coordinates
    7. Practice
  14. 13Sequences, Probability, and Counting Theory9 pages
    1. Introduction to Sequences, Probability and Counting Theory
    2. 13.1Sequences and Their Notations
    3. 13.2Arithmetic Sequences
    4. 13.3Geometric Sequences
    5. 13.4Series and Their Notations
    6. 13.5Counting Principles
    7. 13.6Binomial Theorem
    8. 13.7Probability
    9. Practice
  15. Appendices1 page
    1. AProofs, Identities, and Toolkit Functions