This chapter is the first of two dedicated to trigonometric identities, equivalency statements that will serve as tools for future chapters and mathematics courses. The preceding chapters focus on a concrete representation of trigonometric functions—how they are defined in terms of right triangles, how they derive their values from the unit circle, and how they are affected graphically with the introduction of real number values. In order to master more advanced trigonometric theorems, however, you must first focus on comparatively more abstract concepts.
The first six chapters of the book may have felt a little like geometry, but the next clump of chapters will feel more like algebra. This chapter marks the beginning of trig identities, formulas you need to memorize. These formulas allow you to manipulate complicated trig expressions and make them much simpler looking and easier to deal with. And don’t worry about having to commit even more things to memory—unlike the unit circle, you’ll use these formulas so much, the memorization will come naturally.
Each new section in this chapter brings a new batch of identities to memorize. Basically, all of the problems in each section will fall into one of two categories:
- Simplifying trig expressions (sort of like simplifying fractions to lowest terms, so that what you end up with is nicer looking than what you started with)
- Verifying identities (where you take an equation that doesn’t look like it could possibly be equal and show that it is)