Glen Van Brummelen tells the story of trigonometry as it evolved from an instrument for understanding the heavens to a practical tool, used in fields such as surveying and navigation.
Modern Trigonometry
Plane Trigonometry: a Modern Approach' 2004 Ed.
New to this edition: The second edition has been comprehensively revised over three years Errors have been corrected and some proofs marginally improved The substantial difference is that Chapter 11 has been significantly extended, ...
Modern Algebra and Trigonometry
I haven't followed mathematical proofs with such delight in decades. If, as the author laments, spherical trigonometry was in danger of extinction, this book will give it a long-lasting reprieve.
It has a reputation as a dry and difficult subject, a glorified form of geometry complicated by tedious computation. In this book, Eli Maor draws on his remarkable talents as a guide to the world of numbers to dispel that view.
Trigonometry: A Modern Approach