  The development of the trigonometric functions in introductory texts usually
follows geometric constructions using right triangles or the unit circle. While
these methods are satisfactory at the elementary level, advanced mathematics
demands a more rigorous approach. Our purpose here is to revisit elementary
trigonometry from an entirely analytic perspective. We will give a
comprehensive treatment of the sine and cosine functions and will show how to
derive the familiar theorems of trigonometry without reference to geometric
definitions or constructions.
