Trigonometry

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. Some of the features are: Beginning activities in each section that engage students with the material to be introduced, focus questions that help students stay focused on what is important in the section, progress checks that are short exercises or activities that replace the standard examples in most textbooks, a section summary, and appendices with answers for the progress checks and selected exercises. This text was written for the three-credit trigonometry course at Grand Valley State University (MTH 123 – Trigonometry). This text begins with a circular function approach to trigonometry and transitions to the study of triangle trigonometry, vectors, trigonometric identities, and complex numbers. Important Features of the Textbook This book is meant to be used and studied by students and the important features of the textbook were designed with that in mind. Please see the Note to Students on page (v) for a description of these features. Content and Organization The first two chapters of the textbook emphasize the development of the cosine and sine functions and how they can be used to model periodic phenomena. The other four trigonometric functions are studied in Section 1.6 and Section 2.4. Triangles and vectors are studied in Chapter 3, trigonometric identities and equations are studied in Chapter 4, and finally, using trigonometry to better understand complex numbers is in Chapter 5. Following is a more detailed description of the sections within each chapter. Note to Students Preface The Trigonometric Functions The Unit Circle The Cosine and Sine Functions Arcs, Angles, and Calculators Velocity and Angular Velocity Common Arcs and Reference Arcs Other Trigonometric Functions Graphs of the Trigonometric Functions Graphs of the Cosine and Sine Functions Graphs of Sinusoidal Functions Applications and Modeling with Sinusoidal Functions Graphs of the Other Trigonometric Functions Inverse Trignometric Functions Solving Trigonmetric Equations Triangles and Vectors Trigonometric Functions of Angles Right Triangles Triangles that Are Not Right Triangles Applications of Triangle Trigonometry Vectors from a Geometric Point of View Vectors from an Algebraic Point of View Trigonometric Identities and Equations Trigonometric Identities Trigonometric Equations Sum and Difference Identities Double and Half Angle Identities Sum and Product Identities Complex Numbers and Polar Coordinates The Complex Number System The Trigonometric Form of a Complex Number DeMoivre's Theorem and Powers of Complex Numbers The Polar Coordinate System Answers for the Progress Checks Answers and Hints for Selected Exercises Some Geometric Facts about Triangles and Parallelograms Index