In This Chapter
Tracing the unit circle
Determining coordinates of special angles
Labeling angles with degrees and radians
One of the ways that mathematicians first defined the trig functions was by using ratios formed from the measures of the sides of right triangles (see Chapter 7). Right triangles and the measures of their sides are convenient and easy to construct. This fact led to a sort of natural development of the trig functions, and it proved to be most useful because it allowed engineers, astronomers, and mathematicians to make accurate calculations of the heights of tall objects, areas of large expanses, and predictions of eclipses and other astronomical phenomena. But, of course, they couldn't stop there. The world of trigonometry and its applications opened up even more when they expanded the trig functions and properties to angles of any measure — positive and negative — not just those limited to a right triangle. This extension of the angles allowed them to calculate the areas of triangles containing obtuse angles and conduct navigational plots. The best place to begin describing these new function values ...