Math

Trigonometry

What is trigonometry about?

Trigonometry , as the word itself shows, refers to the measurement of the triangle s. This branch is one of the many that is part of the scientific study of mathematics, in charge of the study of the sine, cosine, tangent, cotangent, secant and cosecant in this sense.

This trigonometry study is applied in situations or spaces where measurement is required in the most precise way possible , that is why this study is applied exactly in geometry. One of the most common uses of trigonometry can be observed in the study of the stars or the stars, measuring the distance between them or between geographical points.

The study of trigonometry dates back to ancient times, even from the era of Egypt and Babylon, it is known that the movement of the planets as well as eclipses were studied . The Egyptians, according to the conclusions that come from many studies, determine that they were based on trigonometry to be able to make the pyramids that we know today as the pyramids of Egypt.

There are some famous people in history who are known for their studies and contributions in this area of ​​trigonometry; among them we can mention:

  • Hipparchus of Nicaea
  • Arybhata
  • Varahamihira
  • Brahmagupta
  • Abu’l-Wafa, among others.

Basic Conceptions of Trigonometry

In order to measure the angle of a certain figure or object, it is necessary to know and use three units, of which we will mention below:

  • Radian : is handled mostly in the area of ​​mathematics.
  • Sexagesimal degree: it is one that is commonly used in daily life.
  • Decimal system: it is used for both construction and topography.

Trigonometric ratios

The ratios obtained from the three sides of a right triangle are known as trigonometric ratios of an angle, that is, the comparison that is made by its quotient of its three sides being in this case a, b, and c.

  • The sine that characterizes the angle a is defined as the ratio obtained between the opposite leg and the hypotenuse.
  • The cosine is defined as the ratio obtained between the contiguous or adjacent leg and the hypotenuse.
  • The tangent is the result defined as the ratio obtained between the opposite leg and the adjacent or contiguous leg.

In this sense, we must point out that:

  • To obtain the  sine  of a fixed angle, the length of the opposite leg and that of the hypotenuse must be divided.
  • The  cosine  is obtained from the relationship between the length of the adjacent leg and the hypotenuse.
  • To obtain the  tangent  , the length of both legs is divided.
  • For the cotangent function,   the length of the adjacent leg is divided by the opposite.
  • For the secant function   , the length of the hypotenuse on the adjacent leg is related.
  • Finally, to determine the cosecant function   , the length of the hypotenuse is divided on the opposite leg.

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