Trigonometry by Michael Corral
Trigonometry - Table of Contents
1. Right Triangle Trigonometry
1.1 Angles
1.2 Trigonometric Functions of an Acute Angle
1.3 Applications and Solving Right Triangles
1.4 Trigonometric Functions of Any Angle
1.5 Rotations and Reflections of Angles
2. General Triangles
2.1 The Law of Sines
2.2 The Law of Cosines
2.3 The Law of Tangents
2.4 The Area of a Triangle
2.5 Circumscribed and Inscribed Circles
3. Identities
3.1 Basic Trigonometric Identities
3.2 Sum and Difference Formulas
3.3 Double-Angle and Half-Angle Formulas
3.4 Other Identities
4. Radian Measure
4.1 Radians and Degrees
4.2 Arc Length
4.3 Area of a Sector
4.4 Circular Motion: Linear and Angular Speed
5. Graphing and Inverse Functions
5.1 Graphing the Trigonometric Functions
5.2 Properties of Graphs of Trigonometric Functions
5.3 Inverse Trigonometric Functions
6. Additional Topics
6.1 Solving Trigonometric Equations
6.2 Numerical Methods in Trigonometry
6.3 Complex Numbers
6.4 Polar Coordinates
Appendix A: Answers and Hints to Selected Exercises
Appendix B: Graphing with Gnuplot
What You Will Learn in Trigonometry
"Trigonometry by Michael Corral" is a free, open-source textbook designed for college and advanced high school students. It focuses on building a "geometric understanding" of trigonometric concepts before introducing analytical methods. The book offers 495 exercises, practical examples, and even a tutorial on using "Gnuplot" for graphing trigonometric functions, making it ideal for both self-learners and classroom use.
Unlike traditional textbooks, Corral’s approach emphasizes visualization and real-world applications. Topics include right and oblique triangles, trigonometric identities, inverse functions, and numerical methods like the secant method. Each chapter develops intuition step-by-step, helping learners see how trigonometry connects with geometry and algebra rather than treating it as a set of abstract formulas.
Because it’s released under a "GNU Free Documentation License", the book is completely free to download and adapt for personal or educational purposes. Its combination of clarity, geometric focus, and computational tools makes it an excellent resource for students seeking a strong conceptual foundation in trigonometry without expensive textbooks.
Book Details & Specifications
Title:
Trigonometry by Michael Corral
Publisher:
mecmath.net
Year:
2009
Pages:
174
Type:
PDF
Language:
English
ISBN-10 #:
1475074573
ISBN-13 #:
978-1475074574
License:
GNU
Amazon:
Amazon
About the Author: Michael Corral
The author
Michael Corral
is a mathematics educator and author known for creating open-source textbooks like "Trigonometry" and "Vector Calculus". He teaches at Schoolcraft College and holds degrees in Mathematics and Industrial & Operations Engineering from the University of Michigan. His writing style emphasizes clarity, "geometric intuition", and practical problem-solving over dense theoretical explanations.
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