Millions of students worldwide learn trigonometry every year as a rite of passage in science, technology, engineering, and mathematics (STEM) education. They pass through a precalculus course, or even a course specifically focused on trigonometry, that is typically wedged between their introductions to the more fundamental skills in algebra and the more advanced training they will receive in differential and integral calculus. These experiences in the study of mathematics are generally directed to provide students with a working knowledge of the algebraic, geometric and analytic fundamentals that have become associated with the six trigonometric functions. Given the ever-escalating pressures to accelerate student training in these subjects, motivation for the study of trigonometry often receives short shrift. And when students present the natural question “why?”, the responses are meager and unprepared: “you’ll see when you study X later.”

So, who decided that degrees would be divided into sixties rather than tenths, as is everything else in scientific measurement? Is trig about triangles, or circles? What’s the deal with periodicity? Why is the sine function so important?

The classroom unit In this unit, students are introduced to the basic elements of the geometry of the circle and the measure of its arcs, central angles and chords, whose interrelationships formed the foundation for trigonometry as a tool for Greek astronomy. Students read a brief excerpt from Claudius Ptolemy's |
Figure 1. Hipparchus of Rhodes,Convergence Portrait Gallery. |

Figure 2. Modern Reconstruction ofHipparchus' Table of Chords. |
The unit As mentioned above, the unit |