Trigonometric ratios are relationships that can be established between the sides of a right triangle.
The first step that is necessary to take before establishing the meaning of the term trigonometric ratios is to determine the etymological origin of the two words that give it shape:
-Reasons derives from Latin, from "ratio", which is synonymous with "reason".
-Trigonometric, for its part, has a Greek origin. It means "relating 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".
What are trigonometric ratios?
Trigonometry is the name of the branch of mathematics that is dedicated to performing calculations linked to the elements of a triangle . For this, it works with units such as the sexagesimal degree (used when dividing a circle into 360 sexagesimal degrees), the centesimal degree (the division is carried out in 400 centesimal degrees) and the radian (which is taken as the natural unit of angles). and points out that the circumference can be divided into 2 pi radians).
The notion of trigonometric ratio refers to the links that can be established between the sides of a triangle that has an angle of 90º . There are three major trigonometric ratios: tangent , sine and cosine .
To calculate trigonometric ratios you must know the concepts of leg and hypotenuse.
Classification according to type
The trigonometric tangent ratio is the ratio between the opposite leg and the adjacent leg . The sine , for its part, is the ratio between the opposite leg and the hypotenuse , while the cosine is the ratio between the adjacent leg and the hypotenuse .
To understand these trigonometric ratios, of course, you have to know what the legs and hypotenuse are. The adjacent leg is the one that passes through the ninety degree angle, while the opposite leg is precisely the one opposite to the angle. Both, therefore, make up the 90º angle. The hypotenuse , on the other hand, is the longest side of the triangle.
Beyond the tangent, the sine and the cosine, it is possible to recognize other trigonometric ratios that are less used, such as the cotangent (the ratio between the adjacent leg and the opposite leg), the cosecant (the ratio between the hypotenuse and the opposite leg). opposite) and the secant (the ratio between the hypotenuse and the adjacent leg).
Trigonometric ratios in circles
However, we cannot ignore that trigonometric ratios also exist in a circle. In this case, various data of interest and importance must be taken into account, such as these:
-The goniometric circle is the one whose center is at the origin of the coordinates, while its radius is unity.
-In said circle, 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.