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 / hypotenuse
Cosine = 3.4 / 4
Cosine = 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).