4.3 Trigonometry

Trigonometry is the study of triangles, angles, and length. The Greek word trig¯onon means ‘‘triangle’’ and metron means ‘‘measure.’’ For the most part we restrict ourselves to triangles with hypotenuse equal to 1, and so within the unit circle.

4.3.1 The fundamental functions

Many people have heard that a circle has 360 degrees, also written 360°. Why 360? If you look around the web you’ll find stories about ancient Mesopotamians, Egyptians, and base 60 number systems. Whatever the reason, 360 is a great number because it is divisible by so many other numbers like 2, 3, 4, 5, 6, 8, 10, 12, 15, and so on. That is, it’s easy to work with portions of 360° that are nice round whole numbers.

Degrees don’t really have a natural meaning in mathematics though. They are simply a convenient unit of measurement. Instead, we use radians.

A circle of radius r has circumference...