The area of trigonometry, in one form or another, has existed in mathematics for hundreds of years.
Rather than detailing such a history in this text, my desire is to access the power of the World Wide Web (via Netscape) and refer to an excellent source of mathematical history which is located in Scotland.
The source is the MacTutor History of Mathematics Archive at the University of St. Andrews. Their mathematical history of trigonometry provides an impressive synopsis of the background of this subject. I strongly encourage you to visit this site at your leisure and enjoy the many wonderful offerings at the MacTutor History of Mathematics Archive.