In Chapter 3, you familiarize yourself with the most commonly used angles in trigonometry. However, applications in the real world are rarely limited to angles that follow precise, predictable patterns. In this chapter, you explore strategies that analyze angles of any measurement. You begin by calculating reference angles and coterminal angles, which allow you to express angle measurements more manageably.
Did you wonder why the trig tables in Appendix A only covered angles between 0° and 90°? Was it because people in the olden days couldn’t conceive of anything bigger than a right angle? Nope. Here’s the real reason (drumroll please): No matter how big and ugly an angle is, you can find an angle between 0° and 90° that has the same cosine and sine values (and therefore the same tangent, cotangent, secant, and cosecant values as well). There’s no need for a trig table that’s 32 pages long when you can settle for one that’s a quarter the size. Genius!
Why bother rewriting angles at all, you ask? It allows you to apply everything you learned about right triangle trig (in Chapters 2 and 3) to angles of any shape and size.