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 , cosineand 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


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  .
  • 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


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


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 .

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