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Chapter 23

# 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

A big 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). And you'll also find some alternate notation and optional formats.

## Reciprocal Identities

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

and

An alternate way of writing these identities uses an exponent of –1 rather than a fraction:

sin θ = (csc θ)−1 and csc θ = (sin θ)−1

Note that the exponents apply to the entire function. These are not the inverse functions: csc−1 θ and sin−1 θ.

Secant, cosecant, and cotangent are technically the three reciprocal functions, but you can write identities to show their reciprocals, ...

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