What is cosecant?

What Does cosecant Mean

Cosecant is the inverse function of the sine of an arc or an angle. It is a concept that is used in the field of trigonometry , a branch of mathematics linked to geometry.

To understand what the cosecant is, you first have to know what the sine is. This function , in a right triangle, is obtained by dividing the leg opposite an acute angle and the hypotenuse. It should be remembered that the hypotenuse is the longest side of a right triangle, while the other two sides are called legs .
Therefore, if the sine is equal to the opposite leg divided by the hypotenuse, the cosecant is obtained by dividing the hypotenuse by the opposite leg since it is the inverse function. The same result is reached by obtaining the quotient of 1 and the sine .

In a right triangle whose hypotenuse is 10 centimeters and the opposite leg is 4 centimeters, the cosecant will be equal to 2.5:
Cosecant = Hypotenuse / opposite leg

Cosecant = 10/4

Cosecant = 2.5
This can be checked by dividing 1 and the sine. If the sine is equivalent to the opposite leg divided the hypotenuse:
Sine = Opposite Leg / Hypotenuse

Sine = 4/10

Sine = 0.4
And later:
Cosecant = 1 / Sine

Cosecant = 1 / 0.4

Cosecant = 2.5
It should be noted that the relationship between the cosecant and the sine is similar to that maintained by the cosine function with its inverse, the secant , and the link established by the tangent function and the cotangent (its inverse).
Since all these functions are practically impossible to solve mentally for most people, and since in everyday calculations the values ​​of the given angles are usually more or less the same, it is possible to make a table with the cosecant of the most common angles. common, among which are the null (0 °), 30 °, 90 ° and 270 °, among others that appear in the second image of this definition, with their magnitudes both in degrees and radians .
It is important to understand that the cosecant may seem too abstract compared to other parts of the world of numbers when viewed from most people's use of mathematics in their everyday lives, but it is a very useful function that It has practical applications to solve different problems that do affect our day to day, even if we do not know it.
For example, both the cosecant and the rest of the functions mentioned above are used very frequently in the field of computer programming, to solve problems when developing a video game or an animated film in three dimensions. Let us not forget that behind the computer-generated images there are millions of geometric figures , the triangle being the most important, and it is precisely the latter that especially takes advantage of the cosecant to solve, for example, the values ​​of its sides.

Triangles, in turn, have more than one application in the world of three-dimensional graphics: on the one hand, they are the basis of models, that is, of characters and settings, since they are built from them, although once several rendering techniques have been applied, their presence is hardly noticeable and the surfaces take on a "soft" appearance; but the triangle can also serve as an imaginary guide to compute the position of a point after a certain translation, and that is where the use of the cosecant can help us.
For example, if we have a right triangle of which we know one of its angles and its opposite side, we can start by elaborating the cosecant equation of the angle = hypotenuse / opposite to find out the value of the hypotenuse, since we know the other two.

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