Chapter 10
Introducing Basic Identities
IN THIS CHAPTER
Recognizing reciprocal identities
Putting functions head-over-tails by using ratio identities
Performing attitude adjustments on negative angles
Relating functions to Pythagoras’s way of thinking
Using multiple identities to simplify matters
I’m sure a thousand questions are running through your mind: What’s a trig identity? Is it possible to have a mistaken trig identity? Does anyone commit trig-identity theft? Can you have an identity crisis with trig? The answer: No — probably not.
Trig identities aren’t nearly as sinister as you may think. They’re actually very helpful tools in simplifying trig expressions and solving equations. These identities are special to trigonometry. Basically, they’re equivalences — they give you options to substitute into equations in order to simplify. For example, wouldn’t you rather use the number 1 than ? Of course! In most cases, the number 1 is simpler. That’s how trig identities work — they ...
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