# Defined and Reciprocal Functions

## Defined and Reciprocal Functions

We are going to take a look at **defined and reciprocal functions**. Let’s just take the tangent function, for example. The tangent function is defined as the ratio of the sine to the cosine, so if we’re looking for a tangent, which can be abbreviated as tan, to find the tangent of x, we divide the sine of x by the cosine of x, so that’s just a normal trigonometric function.

Now, say we’re looking for the **reciprocal**. To find the reciprocal of a number, that means to place the number as the **denominator** of a fraction with a numerator of 1. Say we were looking for the reciprocal of tangent, we would take tangent, we would put it in the denominator of a fraction, and give it a numerator of 1.

That’s what’s been done right here, (all right) so these are all reciprocal functions and these reciprocal functions are for sine, cosine, and tangent. For example, we have **cosecant** which is abbreviated csc. To find the reciprocal of sine, we take sine, and remember, we put it in the denominator of a fraction and give it a numerator of 1.

That’s what we’ve done right here, we put sine in the bottom, we’ve given it a numerator of 1, so the reciprocal of sine is what is equal to cosecant. Now, secant is basically the reciprocal of cosine, so when we find the reciprocal of cosine, we call it secant, and secant can be abbreviated sec.

Then we have **cotangent**, which is abbreviated cot, and what cotangent is it’s just the reciprocal of tangent. Here we have tangent in the denominator with a numerator of 1. Reciprocal functions are defined quite simply, as long as you got to remember that you just take the number, you put it in the denominator, and give it a numerator of 1.

Just remember that’s always how you find the reciprocal of a number. Now, it’s important to know these 3 reciprocal functions that I just told you. Though, remember that these reciprocal functions go back to the basic functions of tangent, sine, and cosine. It’s important to focus on tangent, cosine, and sine because those are the most important functions, but remember that there are reciprocal functions out there, but they’re not going to be used as commonly as the three basic functions.