Author Profile

Matthew Stephens is an Adjunct Faculty member of the Department of Mathematics at Schoolcraft College. He received a B.A. in Mathematics from the University of California at Berkeley, and received an M.A. in Mathematics and an M.S. in Industrial & Operations Engineering from the University of Michigan. Stephens conducted postdoctoral research with Peter Donnelly at the University of Oxford. Stephens was awarded the Guy Medal (bronze) in 2006. He was elected a Fellow of the Royal Society in 2023.

About The Book

This college level trigonometry text may be different than most other trigonometry textbooks. In this book, the reader is expected to do more than read the book but is expected to study the material in the book by working out examples rather than just reading about them. So the book is not just about mathematical content (although it does contain important topics in trigonometry needed for further study in mathematics), but it is also about the process of learning and doing mathematics and is designed not to be just casually read but rather to be engaged. Recognizing that actively studying a mathematics book is often not easy, several features of the textbook have been designed to help students become more engaged as they study the material. This book will provide a welcome resource for students seeking an undergraduate text on advanced trigonometry, when few are readily available. Ideal for selfstudy, this text offers a clear, logical presentation of topics and an extensive selection of problems with answers. The book covers all areas of trigonometry including the theory and equations of tangent, sine and cosine, using trigonometry in three dimensions and for angles for any magnitude, related to triangles. Everything you will need is here in this one book. Each chapter includes not only an explanation of the knowledge and skills you need, but also worked examples and test questions. This book represents a novel approach for the trigonometry and an original scientific work in this field, by using the ensemble structure composed of the real analysis and the axiomatic fundaments of geometry. Throughout this book one presents, in a proper manner, definitions, properties, formulae and applications more specific of the subject title and its immediate connections. The book is recommended as a pertinent introduction for the university students, mathematics teachers and anyone who is interested in the major elements regarding the essence of real mathematics.

Table of Contents

Preface
Chapter 1. Basics of Angles and Triangles
Chapter 2. Introduction to Trigonometric Ratios
Chapter 3. Trigonometric Identities
Chapter 4. Trigonometric Ratios of Compound Angles
Chapter 5. Trigonometric Ratios of Multiple and Sub-Multiple Angles
Chapter 6. Inverse Trigonometric Functions
Chapter 7. Graphs of Trigonometric Functions
Chapter 8. Trigonometric Equations
Chapter 9. Heights and Distances
Chapter 10. Applications of Trigonometry
Bibliography