The cosine is a trigonometric function.
The idea of cosine 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 its dictionary. The official abbreviation of this trigonometric function is cos , and this is how we find it in equations and calculators.
It should be noted that the sine is the result of dividing the leg that is opposite to an angle and the hypotenuse (in a right triangle, the longest side is the hypotenuse, while the other two - which form the 90º angle - are called legs ). The complement, for its part, is the angle that, added to another, completes an angle of 90° .
Cosine and trigonometry
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 cosecant.
In secondary school, trigonometry is usually included in the last stage of the program, as it is a very complex part and difficult to understand for those who do not have a legitimate taste for numbers. Its 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 carry out measurements with a high degree of precision .
The law of cosines is a generalization of the Pythagorean theorem.
Possible calculations
Suppose we have a right triangle ABC , with one angle of 90º and two angles of 45º . By dividing one of the opposite legs at an angle of 45º and the hypotenuse, we will obtain the sine and then we can calculate the cosine.
Another simpler way to calculate the cosine in a right triangle is by dividing the leg adjacent to an acute angle and the hypotenuse . The sine , for its part, is obtained by dividing the leg opposite the hypotenuse, while the tangent involves the division of the opposite leg and the adjacent leg. These three functions (cosine, sine and tangent) are the most relevant in 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 leg / hypotenuse
Cosine = 3.4 / 4
Cosine = 0.85
The secant function , on the other hand, involves dividing 1 by the cosine. In the example above, the secant is 1.17 .
law of cosines
The law of cosines , 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 that 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 shown in the image: c squared is equal to the sum of a squared and b squared, minus twice the product ab cosγ .
Other definitions
Another way to define the cosine is to understand it as:
* an even function : in mathematics, this classification is given to real variable functions taking into account their parity . There are three possibilities: they can be even, odd or have no parity;
* a continuous function : this is a mathematical function in which the points close to the domain carry a series of small variations in their values;
* a transcendent function : it 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 with each other).