Summary: The study of trigonometry suffers from a basic dichotomy that presents a serious obstacle to many students. On the one hand, there is triangle trigonometry, in which angles are commonly measured in degrees and trigonometric functions are defined as ratios of sides of a right-angled triangle. On the other hand, there is circle trigonometry, in which angles are commonly measured in radians and trigonometric functions are expressed in terms of the coordinates of a point on the unit circle centered at the origin. Faced with two such distinct conceptual approaches to trigonometry, is it any wonder that so many students get confused? Once students begin to use the sine and cosine as examples of periodic functions, circle trigonometry dominates, but there is a tradition that triangle trigonometry is the simpler and more basic form and that students need to be grounded in this before being introduced to circle trigonometry. This article provides a historical overview of the development of trigonometry. This historical overview presents an argument for beginning the study of trigonometry with the circle definitions of the trigonometric functions and angle measurement. (Contains 18 figures.) (ERIC)