Rather than dividing a circle into some number of segments (like 360 degrees), mathematicians often prefer to measure angles using the circumference of a unit circle - a circle with radius 1. This way of measuring angles is called...

Here is a site that clearly and thoroughly explains the radian measure of angles. There are example problems solved, problems for the student to attempt, and answers to the student problems.

The Clark University site shows and explains the graphs of the six trigonometric functions. It explains how to find an arbitrary angle measurement using trig. Also, it explains that sine and cosine functions are complementary.