This trigonometry textbook is different than other trigonometry books in that it is free to download, and the reader is expected to do more than read the book and is expected to study the material in the book by working out examples rather than just reading about them. So this book is not just about mathematical content but is also about the process of learning and doing mathematics. That is, this book is designed not to be just casually read but rather to be engaged.

Since this can be a difficult task, there are several features of the book designed to assist students in this endeavor. In particular, most sections of the book start with a beginning activity that review prior mathematical work that is necessary for the new section or introduce new concepts and definitions that will be used later in that section. Each section also contains several progress checks that are short exercises or activities designed to help readers determine if they are understanding the material. In addition, the text contains links to several interactive Geogebra applets or worksheets. These applets are usually part of a beginning activity or a progress check and are intended to be used as part of the textbook.

The authors are very interested in constructive criticism of the textbook from the users of the book, especially students, who are using or have used the book. Please send any comments you have to trigtext@gmail.com.

Access also available here: https://scholarworks.gvsu.edu/books/12/

Table of Contents:

Chapter 1: Triangles and Circles
Introduction to Triangles and Circles
1.1 Triangles and Angles
1.2 Similar Triangles
1.3 Circles
Chapter 1 Summary and Review
Exercises: 1.1 Triangles and Angles
Exercises: 1.2 Similar Triangles
Exercises: 1.3 Circles
Exercises: Chapter 1 Review Problems

Chapter 2: Trigonometric Ratios
Introduction to the Trigonometric Ratios
2.1 Side and Angle Relationships
2.2 Right Triangle Trigonometry
2.3 Solving Right Triangles
Chapter 2 Summary and Review
Exercises: 2.1 Side and Angle Relationships
Exercises: 2.2 Right Triangle Trigonometry
Exercises: 2.3 Solving Right Triangles
Exercises: Chapter 2 Review Problems

Chapter 3: Laws of Sines and Cosines
Introduction to Laws of Sines and Cosines
3.1 Obtuse Angles
3.2 The Law of Sines
3.3 The Law of Cosines
Chapter 3 Summary and Review
Exercises: 3.1 Obtuse Angles
Exercises: 3.2 The Law of Sines
Exercises: 3.3 The Law of Cosines
Exercises: Chapter 3 Review Problems

Chapter 4: Trig Functions
Introduction to Trigonometric Functions
4.1 Angles and Rotation
4.2 Graphs of Trigonometric Functions
4.3 Periodic Functions
Chapter 4 Summary and Review
Exercises: 4.1 Angles and Rotation
Exercises: 4.2 Graphs of Trigonometric Functions
Exercises: 4.3 Periodic Functions
Exercises: Chapter 4 Review Problems

Chapter 5: Equations and Identities
Introduction to Equations and Identities
5.1 Algebra with Trigonometric Ratios
5.2 Solving Equations
5.3 Trigonometric Identities
Chapter 5 Summary and Review
Exercises: 5.1 Algebra with Trigonometric Ratios
Exercises: 5.2 Solving Equations
Exercises: 5.3 Trigonometric Identities
Exercises: Chapter 5 Review Problems

Chapter 6: Radians
Introduction to Trig Radians
6.1 Arclength and Radians
6.2 The Circular Functions
6.3 Graphs of the Circular Functions
Chapter 6 Summary and Review
Exercises 6.1 Arclength and Radians
Exercises 6.2 The Circular Functions
Exercises 6.3 Graphs of the Circular Functions
Exercises: Chapter 6 Review Problems

Chapter 7: Circular Functions
Introduction to Circular Functions
7.1 Transformations of Graphs
7.2 The General Sinusoidal Function
7.3 Solving Equations
Chapter 7 Summary and Review
Exercises 7.1 Transformations of Graphs
Exercises 7.2 The General Sinusoidal Function
Exercises 7.3 Solving Equations
Exercises: Chapter 7 Review Problems

Chapter 8: More Functions and Identities
Introduction to More Functions and Identities
8.1 Sum and Difference Formulas
8.2 Inverse Trigonometric Functions
8.3 The Reciprocal Functions
Chapter 8 Summary and Review
Exercises: 8.1 Sum and Difference Formulas
Exercises: 8.2 Inverse Trigonometric Functions Exercises
Exercises: 8.3 The Reciprocal Functions Exercises
Exercises: Chapter 8 Review Problems

Chapter 9: Vectors
Introduction to Vectors
9.1 Geometric Form
9.2 Coordinate Form
9.3 The Dot Product
Chapter 9 Summary and Review
Exercises: 9.1 Geometric Form
Exercises: 9.2 Coordinate Form
Exercises: 9.3 The Dot Product
Exercises: Chapter 9 Review Problems

Chapter 10: Polar Coordinates and Complex Numbers
Introduction to Polar Coordinates and Complex Numbers
10.1 Polar Coordinates
10.2 Polar Graphs
10.3 Complex Numbers
10.4 Polar Form for Complex Numbers
Chapter 10 Summary and Review
Exercises: 10.1 Polar Coordinates
Exercises: 10.2 Polar Graphs
Exercises: 10.3 Complex Numbers
Exercises: 10.4 Polar Form of Complex Numbers
Exercises: Chapter 10 Review Problems

This textbook was created through Connecting the Pipeline: Libraries, OER, and Dual Enrollment from Secondary to Postsecondary, a $1.3 million project funded by LOUIS: The Louisiana Library Network and the Institute of Library and Museum Services. This project supports the extension of access to high-quality post-secondary opportunities to high school students across Louisiana and beyond by creating materials that can be adopted for dual enrollment environments. Dual enrollment is the opportunity for a student to be enrolled in high school and college at the same time.

The cohort-developed OER course materials are released under a license that permits their free use, reuse, modification and sharing with others. This includes a corresponding course available in Moodle and Canvas that can be imported to other platforms.

These Trigonometry lecture videos coterminal angles, trig functions, quadrantal angles, special acute angles, co-functions, finding theta, reference angles, trig functions, radian measure, arc length, area of a sector, graphing sine and cosine using t-table, amplitude and frequency, phase shift for sine and consine, vertical shift, tangent curve, cotangent transformations, evaluating trig identities, trig expressions, sum and difference for cosine, double and half angle identities, inverse, principal values, solving difficult trig equations, law of cosines, area of a triangle, and vectors and bearing.