ABSTRACT
A common complaint of students is that they will never make use of the mathematics they learn in school. Trigonometry is an area of mathematics that, in fact, they will most probably use in their lifetime and whose applications are numerous. The Fourier Transform, which is based on sine functions and cosine functions, is one of the primary mathematical tools used in many modern devices such as portable phones, digital cameras, digital TVs, computer image processing, the Internet, satellite communications, teleconferencing systems, and compact disc players. The traditional trigonometric concepts examine how trigonometric functions can be used to solve cubic equations and form Lissajous curves. This chapter shows how vectors can be used to prove geometric theorems that students usually encounter in their study of Euclidean geometry. It examines some of the other unmeasurable distances that trigonometry has helped us find. The chapter provides some difficult engineering problems that can be solved using elementary trigonometric relationships.
