The first step that is necessary to take before entering to establish the meaning of the term trigonometric ratios is to determine the etymological origin of the two words that give it shape:

-Razones derives from Latin, from “ratio”, which is synonymous with “reason”.

-Trigonometric, meanwhile, has a Greek origin. It means “related to trigonometry”, and is composed of the following elements of that language: the noun “trigonon”, which can be translated as “triangle”; the name “metron”, which is equivalent to “measure”, and the suffix “-ico”, which means “relative to”.

Right triangle

Trigonometric ratios are relationships that can be established between the sides of a right triangle.

What are trigonometric ratios

Trigonometry is the name of the branch of mathematics that is dedicated to performing calculations linked to elements of a triangle. For this it works with units such as sexagesimal degree (used when dividing a circumference into 360 sexagesimal degrees), the centesimal degree (the division is made in 400 grads) and the radian (which is taken as the natural unit of angles and indicates that the circumference is capable of division into 2 pi radians).

The notion of trigonometric ratio refers to the links that can be established between the sides of a triangle which has an angle of 90º. There are three great trigonometric ratios: tangent, breast and cosine.


To calculate the trigonometric ratios, one must know the concepts of leg and hypotenuse.

Classification according to type

The tangent trigonometric ratio is the reason existing between Hick opposite and the adjacent leg. The breast, meanwhile, is the ratio between the Hick opposite and the hypotenuse, Meanwhile he cosine is the reason between adjacent leg and the hypotenuse.

To understand these trigonometric ratios, of course, you have to know what the legs and the hypotenuse are. The adjacent leg is the one that passes through the ninety degree angle, while the Hick opposite It is precisely the opposite of the angle. Both, therefore, make up the 90º angle. The hypotenuseInstead, it is the longest side of the triangle.

Beyond the tangent, sine and cosine, it is possible to recognize other trigonometric ratios that are less used, such as cotangent (the ratio between the adjacent leg and the opposite leg), the cosecant (the ratio between the hypotenuse and the opposite leg) and the drying (the ratio between the hypotenuse and the adjacent leg).

Trigonometric ratios on circumferences

However, we cannot ignore that trigonometric ratios also exist in a circle. In this case, you have to take into account various data of interest and importance such as these:

-The goniometric circumference is the one that has its center in what is the origin of the coordinates, while its radius is the unit.

-In said circumference, what the aforementioned coordinate axes do is delimit four quadrants, appearing similar triangles.

-As for the trigonometric ratios that can take place in general, we can determine that there are different types of relationships, such as supplementary angles, complementary angles, opposite angles, angles that differ by 180º, angles greater than 360º, negative angles, those that add up to 270º and even those that differ by 90º, among other modalities.

-There are also in this case trigonometric ratios of the half angle or the so-called double angle.