# Drying

Trigonometry is one of the subdivisions of **mathematics** that is responsible for calculating the **elements** that **triangles** have . And it is for this reason that he is dedicated to studying the relationships that may exist between the **angles** and the **sides** of **triangles** . There are six important functions that are considered to be the core of trigonometry. Three of them are classified as the main ones and they are the **sine** , **cosine**and tangent. The other three trigonometric functions are less frequent but just as important and their calculation is not as easily found as in the case of the first three that can be found by means of a calculator, and these are the **secant** , the **cosecant** and the **cotangent** .

## What is the blotter?

In a right triangle we can say that the **secant** is a **trigonometric** function that refers to the **length** that exists in the **hypotenuse** and that is divided by the **length** of **the adjacent side** .

- Definition
- Characteristics of the secant
- What is it for
- How the secant is calculated
- Derivative
- Integral
- Secant domain and range
- Inverse function

## Definition

The definition of **trigonometric ratios** , such as the secant, refers to the links that can be established between the **different sides of** a **triangle** that has an angle of 90º. Among these reasons we can find, apart from the three main ones, three different ones that are known as **reciprocal trigonometric** ratios , among them we have the case of the **secant** .

The secant of an angle is defined as the **relationship** that exists between the **length** of the **hypotenuse** and the length of the **adjacent leg** , in other words:

**sec α = hypotenuse / adjacent**

## Characteristics of the secant

Its main characteristics are the following

- The
**domain**of the secant function is that of the set: {x Є R / x ≠ pi / 2 + n π, n Є Z} - Since sec x ≤ -1 and sec x ≥ 1, we then say that the
**Range**of the**Function**is the**Set R**– (-1,1) - The secant function is
**even**, since sec (-x) = sec x, so the graph is**symmetric**with respect to the y axis. - y = sec x is a
**periodic function**and its Period is**2π**. - The
**function**y = sec x is increasing in the Intervals in which y = cos x is decreasing. y is decreasing when cos x is increasing, that is, in the Intervals [π, 3π / 2) and (3π / 2, 2 π]. - The function y = sec x does not have a
**maximum value**or a**minimum**value and it never**cancels**, that is, it does not have zeros. - y = sec x is a
**continuous**function throughout its domain, that is, in the set. - {x Є R / x ≠ pi / 2 + n π, n Є Z}.

## What is it for

Trigonometric functions, as in the case of the secant, help us to **calculate degrees** , **angles** and other **geometric data** with respect to a certain geometric **figure** . The secant is also used to find the **measure** of the **sides** that **triangle** one has or the measure of its angles as an **inverse** measure that it is.

All these functions have their importance in the study of the **geometry** of the triangles and in the search of forms to represent the **periodic ****phenomena** . They are generally used for **technical calculations** , for land **surveying** and to mark each angle using a certain reference point.

## How the secant is calculated

The secant, which in its abbreviated form is written as **sec** , is the **reciprocal trigonometric** ratio of the cosine , or also its multiplicative inverse and its formula is the following:

**Sec ****α = 1 / cos α ****= c / b**

## Derivative

It is known as the derivative of the secant to the same function that is equal to the secant of the function by the tangent of the function, and by the derivative of the function.

**f (x) = sec w**

**f ‘(x) = (w’ sin w) / cos ^{2} w**

## Integral

The secant integral of a function is derived from that function. We can say that the result of said integral is the **natural logarithm** of the **sum** that occurs between the **secant** and **tangent** of the function. This result cannot be obtained by means of the immediate derivation of a known function.

## Secant domain and range

Domains of both the cosecant and secant as is ** **found **restricted** and can only be used for functions **measures** the **angles** with output numbers that exist. Every time the **terminal** side of an **angle** is along the **X-axis** in which y = 0, the **cosecant function** cannot be performed at that angle.

## Inverse function

In the area of trigonometry, we know the inverse function of the secant of an angle by the name of **arcoscant** . It is symbolized as ** “arsec α”** and its geometric meaning is the angle whose

**secant**is

**alpha**.