Chapter 23

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.

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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