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:
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, ...