# Understanding Trigonometry Terms

Like any math or science topic, trigonometry has its own unique vocabulary. Trigonometry uses functions with names like sine, cosine, and secant, and Greek letters like alpha and beta to represent common angles. To understand how to use this vocabulary, you need to understand the context in which you are using it.

Every triangle has six parts: three sides and three angles. If you measure the sides and then make pairings of those measurements (taking two at a time), you have three different pairings. Do division problems with the pairings — changing the order in each pair — and you have a possible six different answers. These six different answers represent the six trig functions. For example, if your triangle has sides measuring 3, 4, and 5, then the six divisions are 3/4, 4/3, 3/5, 5/3, 4/5, and 5/4.

The six trig functions are named *sine*, *cosine*, *tangent*, *cotangent*, *secant*, and *cosecant*. Many people confuse the spoken word *sine* with sign — you can’t really tell the difference when you hear it unless you’re careful with the context. You can “go off on a tangent” in some personal dealings, but that phrase has a whole different meaning in trig. Cosigning a loan isn’t what trig has in mind, either. The other three ratios are special to trig speak. You can’t confuse them with anything else.

## Use abbreviations for trig functions

Even though the word *sine* isn’t all that long, you have a three-letter abbreviation for this trig function and all the others. Mathematicians find using abbreviations easier, and those versions fit better on calculator keys. The functions and their abbreviations are

As you can see, the first three letters in the full name make up the abbreviations, except for cosecant’s.

## Represent angles using trig notation

Angles are the main focus in trigonometry, and you often don’t know their measure. Many angles and their angle measures have general rules that apply to them. You can name angles by one letter, three letters, or a number, but to do trig problems and computations, mathematicians commonly refer to the angle measures with Greek letters.

The most commonly used letters for angle measures are *a* (alpha), *b* (beta), *g* (gamma), and *q* (theta). Also, many equations use the variable *x* to represent an angle measure.

Algebra has conventional notation involving superscripts, such as the 2 in *x*^{2}. In trigonometry, most superscripts have the same rules and characteristics as in other mathematics. But trig superscripts often look very different. The following table presents a listing of many of the ways that trig uses superscripts.

The first entry in the table shows how you can save having to write parentheses every time you want to raise a trig function to a power. This notation is neat and efficient, but it can be confusing if you don’t know the “code.” The second entry shows you how to write the reciprocal of a trig function. It means you should take the value of the function and divide it into the number 1. The last entry in the table shows how you write the inverse sine function. Using the –1 superscript right after sine means that you’re talking about inverse sine (or arcsin), not the reciprocal of the function.