Pre-Calculus All-in-One For Dummies

Chapter 12

Identifying with Trig Identities: The Basics

IN THIS CHAPTER

Reviewing the basics of solving trig equations

Simplifying and proving expressions with fundamental trig identities

Dealing with trig proofs

In this chapter and the next, you work on simplifying trig expressions. After performing all the possible algebraic simplification, you can often use basic trig identities to further simplify expressions and prove more complicated identities. This chapter covers basic identities, which are statements that are always true and that you use throughout an entire equation to help you simplify the problem, one expression at a time, prior to solving it. And you’re in luck, because trig has many basic identities to choose from.

The biggest challenge you’ll find when simplifying trig expressions by using trig identities, though, is knowing when to stop. Enter proofs, which give you an end goal so that you know when you’ve hit a stopping point. You use proofs when you need to show that two expressions are equal even though they look completely different. (If you thought you were done with proofs when you moved past geometry, think again!)

Here is some really important advice: Know ...