When it comes to knowing the meaning of the term cotangent, it is necessary, in the first place, to discover what its etymological origin is. In this case, we can state that it is a word that derives from Latin. According to abbreviationfinder.org, 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 that, we find the fact that cotangent means “inverse of the tangent of an arc or of an angle”.
The notion of cotangent refers to the inverse function of the tangent of an arc or an angle. To understand what cotangent is, therefore, we must know what tangent is.
In the context of trigonometry (a specialty of mathematics), the tangent of a right triangle is obtained by dividing the leg opposite an acute angle and the adjacent leg. It should be remembered that the longest side of these triangles is called the 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 ratio of the opposite leg to the adjacent leg, the cotangent is equal to the ratio of the adjacent leg to 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
Leg Cotangent = 15 / 12
Cotangent = 1.25
Since the cotangent is the inverse function of the tangent, it can also be obtained by dividing 1 by the tangent. In our previous example, the tangent equals 0.8 (the result of the division between the opposite leg and the adjacent leg). Therefore:
Cotangent = 1 / tangent
Cotangent = 1 / 0.8
Cotangent = 1.25
Within the field of mathematics, and more specifically in the field of trigonometry, the cotangent plays an important role. Specifically, we talk about what the properties of the cotangent function are. And these are none other than continuity, domain, range, decreasing or period, for example.
Just as cotangent is the inverse of tangent, cosecant is the inverse of sine, and secant is the inverse of cosine.
In the same way, we cannot ignore the existence of what is known as a hyperbolic cotangent. This 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 top of that there is what is called addition theorem. A theorem that comes to expose the way to be able to synthesize that aforementioned hyperbolic tangent.
