The purpose of this book is to provide a way of trigonometry that is simple, intuitive, and where it is clear where the ideas come from. In most trigonometry classes, the material is simply thrown at the student, with no explanation as to why anything is. Here, it is attempted to build the subject from the ground up. At the same time, it tries to avoid anything overly rigorous. There is no need for advanced, perfect, research-quality proofs at every step. However, there is an appendix with some details on how to write a good proof. The student should have an understanding of basic algebra and geometry, however, as much is explained in the book as possible. The last chapter contains an application of calculus to trigonometry; this section is not necessary for learning the subject, but does require knowledge of calculus.
The book starts from the very basics, explaining the conversion between radians and degrees, then progressing through the trigonometric functions, the unit circle, trigonometric identities and solving trigonometric equations, graphing trigonometric functions, and finally, the application of calculus to trigonometry. Problems are included at the end of each chapter, to check one's understanding of the material; solutions to the problems are provided in Appendix 1.
Hopefully this book will more easily guide you through trigonometry, and act as both a self-learning resource and a good accompaniment to whatever classes you may be taking.