In This Chapter
Assigning trig function values from the unit circle
Using reference angles and terminal sides
Using coordinates to calculate trig functions
Defining trig-function domains and ranges
The six basic trig functions all had humble beginnings with the right triangle and its angles. The unit circle opens up a whole new world for the input values into those functions. Because of the nature of trig functions — they repeat the same patterns over and over — the output values show up regularly. This repetition is a good thing; you recognize where in the pattern a particular input belongs and then assign the output. Life is good.
So many angles are used in trigonometry and other math areas, and the majority of those angles are multiples of 30 and 45 degrees. So, having a trick up your sleeve letting you quickly access the function values of this frequent-flier list of angles makes perfect sense. All you need to know or memorize are the values of the trig functions for 0-, 30-, 45-, 60-, and 90-degree ...