The idea of **cosine** it is used in the field of **geometry** . Cosine, in this framework, is the **sine of the complement of an arc or an angle** , indicates the **Royal Spanish Academy** (**RAE** ) in your dictionary. The official abbreviation of this trigonometric function is **cos** , and in this way we find it in the equations and in the calculators.

It should be noted that the **breast** it is the result of dividing the **leg that is opposite an angle** and the **hypotenuse** (In a right triangle, the major side is the hypotenuse, while the other two - which form the 90º angle - are called legs). The complement, meanwhile, is the angle that, adding to another, completes a **90 ° angle** .

These concepts belong to the branch of mathematics known as **trigonometry** , which focuses on the analysis of the so-called *trigonometric ratios*, among which are the following four, in addition to the sine and cosine: tangent, secant, cotangent and reaping.

In high school, trigonometry is usually included in the last stage of the program, since it is a very complex and difficult part to understand for those who do not have a legitimate taste for numbers. His intervention in the rest of the branches of mathematics is sometimes direct, and other times, indirect; Broadly speaking, we can say that its application takes place whenever it becomes necessary to perform measurements with a high degree **prescission** .

Suppose we have a right triangle **ABC** , with a **angle** from **90º** and two angles of **45º** . Dividing one of the opposite legs at an angle of **45º** and the hypotenuse, we will get the sine and then we can calculate the cosine.

Another simpler way to calculate the cosine in a right triangle is **dividing the leg adjacent to an acute angle and the hypotenuse** . He **breast** , on the other hand, is obtained by dividing the opposite leg to the hypotenuse, while the **tangent** it implies the division of the opposite leg and the adjacent leg. These three functions (cosine, sine and tangent) are the most relevant of the ** trigonometry** .

If a triangle has a hypotenuse of 4 centimeters, an opposite leg of 2 centimeters and an adjacent leg of 3.4 centimeters, its cosine will be **0,85** :

*Cosine = Adjacent cathetus / hypotenuseCosine = 3.4 / 4Cosine = 0.85*

The **function** **drying** , on the other hand, implies the division of 1 by the cosine. In the previous example, the secant is **1,17** .

The **cosine law** , which is also known as the **cosine theorem** , is a generalization of the well-known Pythagorean theorem. This is the relationship that can be established between one of the sides of a right triangle with the remaining two and with the cosine of the angle they form.

In a **triangle** **ABC** with the angles **α, β, γ** and the sides **a, b, c** (opposite to the previous ones, in respective order), the cosine theorem can be defined as seen in the image: **c** squared equals the sum of **to** squared and **b** squared minus twice the product **ab cosγ** .

Another way to define the cosine is to understand it as:

*** an even function** : in mathematics, this classification is received by the functions of the real variable taking into account its **parity** . There are three possibilities: they can be even, odd or have no parity;

*** a continuous function** : it is a mathematical function in which points near the domain entail a series of small variations in their values;

*** a transcendent function** : is a function that cannot satisfy a polynomial equation with coefficients that are **polynomials** (A polynomial is an expression composed of a sum of products of constants and variables among themselves).