We explain what trigonometry is, a little history about this branch of mathematics and the most important concepts it uses.
What is Trigonometry?
Trigonometry is, taking into account the etymological meaning of the word, measuring triangles (from Greek trigon and metron). Trigonometry is part of mathematical science and is responsible for studying the trigonometric ratios of sine, cosine, tangent, cotangent, secant and cosecant.
Trigonometry It is used where precise measurement is required and is applied to geometry is special to the study of spheres within spatial geometry. Among the most common uses of trigonometry are the measurement of distances between stars or between geographical points.
See also: Analytical geometry
A little history about trigonometry
Already the scholars of ancient Egypt and Babylon were aware of the theorems about the measurement of similar triangles and the proportions of their sides. It is known that the Babylonian astronomers recorded the movements of the planets and eclipses. The Egyptians, two thousand years before Christ, already used trigonometry in a primitive way to build their pyramids.
The foundations of current trigonometry were developed in Ancient Greece, but also in India and in the hands of Muslim scholars. Scholars of ancient trigonometry were Hipparchus of Nicaea, Arybhata, Varahamihira, Brahmagupta, Abu'l-Wafa, among others.
The first use of the “sine” function dates back to the 8th century BC. C. in India. The person who introduced the analytical treatment of trigonometry in Europe was Leonhard Euler. They were then known as “Euler formulas”.
They started from the correspondence that exists between the length of the sides of a triangle since they maintain the same proportion. If a triangle is similar then the relationship between the hypotenuse and a leg is constant. If we observe that a hypotenuse is twice as long, then the legs will be.
Most important concepts of trigonometry
Three units are used to measure angles:
- The radian Which is used more than anything in mathematics.
- The sexagesimal degree Most used in daily life.
- The decimal system Used in surveying and construction.
Trigonometry is defined in certain functions that are applied in various fields to measure the relationship between the sides and angles of a right triangle or a circle. These functions are sine, cosine and tangent. Inverse trigonometric ratios can also be performed, namely: cotangent, secant and cosecant.
In order to carry out these operations it is necessary to take into account certain concepts. The side opposite the right angle is called the hypotenuse (h) which is the longest side of the triangle. The opposite leg is the one that is on the opposite side of the angle in question, while we call the one that is next to it adjacent.
- To obtain the breast of a given angle, the length of the opposite leg and that of the hypotenuse must be divided (that is, opposite leg by hypotenuse: a/h).
- He cosine It is obtained from the relationship between the length of the adjacent leg and the hypotenuse (adjacent leg over hypotenuse: a/h).
- To obtain the tangent The length of both legs is divided (that is, the division is carried out: o/a).
- For the function of cotangent The length of the adjacent leg is divided by the opposite leg (understood as: a/o).
- for the function drying the length of the hypotenuse on the adjacent leg is related (that is, h/a).
- Finally to determine the function cosecant The length of the hypotenuse is divided by the opposite leg (thus obtaining: h/o).
See also: Geometric figures
