# College Algebra and Trig

Algebra and Trigonometry provides a comprehensive and multi-layered exploration of algebraic principles. The text is suitable for a typical introductory Algebra & Trigonometry course, and was developed to be used flexibly. The modular approach and the richness of content ensures that the book meets the needs of a variety of programs. Algebra and Trigonometry guides and supports students with differing levels of preparation and experience with mathematics. Ideas are presented as clearly as possible, and progress to more complex understandings with considerable reinforcement along the way. A wealth of examples - usually several dozen per chapter - offer detailed, conceptual explanations, in order to build in students a strong, cumulative foundation in the material before asking them to apply what they've learned.

License:

**Creative Commons Attribution**. This license is considered to be some to be the most open license since it is the least restrictive. It allows reuse, remixing, and distribution (including commercial), only requiring attribution. The content can be remixed into content of other license, but on the other hand it allows the remix to be put under a more restrictive license.Formats:

**PDF**. A Portable Document Format (PDF) file is can be opened using the free Acrobat Reader. It is not an editable format.**HTML**. An HTML file is a web page document. It can be opened by any web browser. It is an editable format.

Openness Rating (0-4): 3

Openness Comments: The book is only editable in OpenStax/Connexions' editing platform or by editing HTML, which makes it somewhat challenging to remix.

- Preface
- 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

- 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

- 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

- 4. Linear Functions
- Introduction to Linear Functions
- 4.1. Linear Functions
- 4.2. Modeling with Linear Functions
- 4.3. Fitting Linear Models to Data

- 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

- 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

- 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

- 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

- 9. Trigonometric Identities and Equations
- Introduction to Trigonometric Identities and Equations
- 9.1. Solving Trigonometric Equations with Identities
- 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

- 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

- 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

- 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

- 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

- 14. Proofs, Identities, and Toolkit Functions

Supplements:

**WebAssign online homework**. WebAssign is a commercial online homework system. It provides randomized, algorithmically generated homework with automated grading of numerical and algebraic answers, similar to MyOpenMath. Question sets have been created for this textbook which can be built into assessment sets by faculty. They provide support, and charge about $25/student.