When it comes to knowing the meaning of the term cotangent, it is necessary, first of all, to discover what its etymological origin is. In this case, we can state that it is a word that derives from Latin. It is exactly the result of the union of three delimited components:

-The prefix “co-”, which can be translated as “together”.

-The verb “tangere”, which means “to touch”.

-The suffix “-nte”, which is used to indicate “agent”.

Starting from all this, we find the fact that cotangent means “inverse of the tangent of an arc or of an angle”.

The notion of **cotangent** alludes to **inverse tangent function** of an arc or an angle. To understand what the cotangent is, therefore, we must know what the **tangent**.

In the context of **trigonometry** (a specialty of mathematics), the tangent of a right triangle is obtained **dividing the leg opposite an acute angle and the adjacent leg**. It should be remembered that the longest side of these triangles is called **hypotenuse**, while the other two are called **legs**.

Returning to the idea of cotangent, we had already mentioned that it is the inverse function of the tangent. Therefore, if the tangent is the **quotient** between the opposite leg and the adjacent leg, the **cotangent** equates to **quotient between the adjacent leg and the opposite leg**.

In a right triangle whose hypotenuse is 20 centimeters, its adjacent leg is 15 centimeters, and its opposite leg is 12 centimeters, we can calculate the cotangent as follows:

*Cotangent = Adjacent leg / Opposite legCotangent = 15/12Cotangent = 1.25*

Since the cotangent is the inverse function of the tangent, it can also be obtained **dividing 1 by the tangent**. In our **example** above, the tangent equals 0.8 (the result of the division between the opposite leg and the adjacent leg). Therefore:

*Cotangent = 1 / tangentCotangent = 1 / 0.8Cotangent = 1.25*

Within the field of mathematics, and more specifically in the field of trigonometry, the cotangent plays an important role. Specifically, it talks about what the properties of the cotangent function are. And these are none other than continuity, dominance, travel, decreasing or period, for example.

Just as the cotangent is the inverse function of the tangent, the **cosecant** is the inverse of **breast** and the **drying**, the inverse of **cosine**.

In the same way, we cannot ignore the existence of what is known as a hyperbolic cotangent. It is another term used in trigonometry in relation to a real number. In that case it is established that it becomes the inverse of the hyperbolic tangent.

It is represented by coth (x) or by cotgh (x) and on that there is what is called the addition theorem. A theorem that comes to expose the way to be able to synthesize this hyperbolic tangent.