The first step before entering fully into the analysis of the meaning of the word trigonometry is to proceed to the establishment of its etymological origin. In this sense we have to state that the aforementioned is in the Greek where we can see how it is formed by the union of trigonon which is equivalent to "triangle", metron which can be defined as "measure" and tria which is synonymous with "three."
The trigonometry is the mathematics subdivision which is responsible for calculating the elements of triangles . For this, he studies the relationships between the angles and the sides of the triangles.
This specialty is involved in various areas of mathematics where you need to work with precision. Trigonometry, however, has a wide variety of applications. It allows, for example, to measure the distances between two locations or celestial bodies from triangulation techniques . Trigonometry is also applied in satellite navigation systems.
There are three units that trigonometry uses to measure angles: the radian (considered as the natural unit of angles, it states that a complete circumference can be divided into 2 pi radians), the gradián or centesimal grade (which allows dividing the circumference into four hundred centesimal degrees) and the sexagesimal grade (It is used to divide the circumference into three hundred and sixty degrees sexagesimal).
The main trigonometric ratios are three: the breast (which consists in calculating the ratio between the opposite leg and the hypotenuse), the cosine (another reason but, in this case, between the adjacent leg and the hypotenuse) and the tangent (the ratio between both legs: the opposite over the adjacent one).
The reciprocal trigonometric ratios, on the other hand, are the cosecant (the reciprocal ratio of the breast), the drying (the reciprocal reason for cosine) and the cotangent (the reciprocal ratio of the tangent).
These are the different kinds of main trigonometric ratios, but we cannot ignore that there are also other fundamental elements within this branch of Mathematics that now concerns us. Specifically, we are referring to the trigonometric ratios of any angle.
The latter would lead us to talk about what is known as a goniometric circumference that is characterized by the fact that its radius is the unit itself and its center is none other than the origin of the relevant coordinates. All this without forgetting that in the same the axes of the coordinates what they do is to delimit four quadrants that are listed in what is the opposite direction to that marked by the hands of a clock.
The trigonometric identity is known as equality that involves trigonometric functions and that are verifiable for any value of the variables (the angles on which the functions are applied).
In addition to all of the above, we cannot ignore the existence of two types of trigonometry. Thus, first, we would have the so-called spherical trigonometry, which is that part of Mathematics that focuses on proceeding to the study of what are spherical type triangles.
Secondly, on the other hand, there is also known as flat trigonometry. In this case, as its name implies, it is that science whose object of analysis and study is the various flat triangles.