Trigonometry For Dummies, 3rd Edition

Chapter 22

Ten Basic Identities … Plus Some Bonuses

IN THIS CHAPTER

Lining up the reciprocal, ratio, Pythagorean, and opposite-angle identities

Tweaking the basic identities

Using building blocks to manipulate trig expressions

Abig advantage of trig expressions and equations is that you can adjust them in so many ways to suit your needs. The basic identities that I list in this chapter are the ones people use most frequently (and remember most often). Secant, cosecant, and cotangent are technically the three reciprocal functions, but you can write identities to show their reciprocals, too. You’ll see other ratios and some extensions of the Pythagorean Theorem. And you’ll also find some alternate notation and optional formats.

Reciprocal Identities

A reciprocal identity is just what the name implies: putting a 1 in the numerator of a fraction and then inserting what it takes to create a reciprocal in the denominator.

Reciprocating the sine

Take a look at the first reciprocal identity and its counterpart:

and

An alternate way of writing these identities uses an exponent of rather ...