# History of trigonometry: emergence and development

Trigonometry history is inextricably linked to astronomy, because for solving this ancient science, scientists began to explore the value of different variables in a triangle.
Today trigonometry is mykrorazdelom mathematics that studies the relationship between the values of angles and lengths of the sides of triangles, and involved analysis of algebraic identities trigonometric functions.
History of trigonometry: emergence and development
The term “trigonometry”
The term, which gave its name to this branch of mathematics, was first discovered in the title of the book authored by a German scientist and mathematician Pytyskusa in 1505. The word “trigonometry” is of Greek origin and means “Measure Triangle”. To be more precise, it is not a literal terms of figures, but of its solution, ie determining values of unknown elements using known.

Trigonometry history began more than two millennia ago. First, its appearance was due to the need to clarify the relationships of angles and sides of a triangle. While studies have shown that the mathematical expression of these relationships requires a special trigonometric functions that are initially processed as numeric table.
For many allied sciences with mathematics impetus to the development of trigonometry was just a story. Origin measurements of angles (degrees) associated with the research scholars of ancient Babylon, is based on a system shestydesyatyrychnuyu calculation, which gave early modern desyatirichnoy, used in many applied sciences.

It is assumed that initially existed as trigonometry of astronomy. Then it was used in architecture. And eventually there was the feasibility of this science in various fields of human activity. In particular, astronomy, sea and air navigation, acoustics, optics, electronics, architecture and others.
Trigonometry at early age
Guided by scientific data on surviving relic, the researchers concluded that the origins of trigonometry associated with the works of Greek astronomer Hipparchus, who first thought on finding ways of solving triangles (spherical). His works belong to the 2nd century BC.
History of trigonometry: origin and development is also one of the most important achievements of that time is to determine the ratio of legs and the hypotenuse in a right triangle, which was later called the Pythagorean theorem.
The history of trigonometry in ancient Greek astronomer associated with the name Ptolemy – geocentric system of the world the author that prevailed before Copernicus.
Greek astronomers were not aware of sine, cosine and tangent. They used tables that allow to find the chord value range using styahayetsya arc. The units were to measure the chord degrees, minutes and seconds. One degree was equal to sixty of the radius.
Also study the ancient Greeks promoted the development of spherical trigonometry. In particular, Euclid in his “Principia” leads theorem on regularity volume ratio of balls of different diameters. His work in this area were a push to develop more and allied disciplines. In particular, the technology of astronomical instruments, theory of map projections, the system of celestial coordinates and t. D.

Ages: the study of Indian scientists
Significant progress achieved medieval Indian astronomers. Death of ancient science in the IV century led to the displacement of the center of mathematics in India.
History of trigonometry as a separate section of mathematical education began in the Middle Ages. That’s when the scientists replaced chord sinuses. This discovery allowed to enter the functions related research sides and angles of a right triangle. That was then beginning vidosoblyuvatysya trigonometry from astronomy, becoming a branch of mathematics.
The first table of sines were Aryabhaty, they were held in 3 of 4 of 5 on. Later versions were detailed tables: in particular, Bhaskara gave a table of sines by 1 on.
History of trigonometry: the emergence and development of the first specialized treatise on trigonometry appeared in X-XI century. The author was his Central Asian scholar al-Biruni. In his main work “Canon Mas’uda” (Book III) by medieval further deepened in trigonometry, resulting sine table (in increments of 15 ‘) and a table of tangents (in increments of 1 °).
The history of trigonometry in Europe
After translation of Arabic treatises in Latin (XII-XIII) the majority of the ideas of Indian and Persian scientists were borrowed European science. The first mention of trigonometry in Europe belong to the XII century.
According to researchers, history of trigonometry in Europe with the name Richard Uollynhfordskoho Englishman who was the author of the work “Four treatise on the direct and inverse chords.” It was the first work of its work, which is entirely devoted to trigonometry. By the XV century, many authors mention in his writings of trigonometric functions.

History of trigonometry: New Era
In modern times, most scientists became aware of the critical importance of trigonometry not only in astronomy and astrology, but in other areas of life. This is, first of all, artillery, optics and navigation in the distant sea expeditions. Therefore, in the second half of the XVI century, the topic of interest of many prominent people of that time, including Nicolaus Copernicus, Johannes Kepler, François Viète. Copernicus took trigonometry several chapters of his treatise “On the rotation of the Heavenly Spheres” (1543). Later, in the 60 years of the XVI century, Retyk – student Copernicus – gives in his book “The optical part of astronomy” pyatnadtsatyznachnye trigonometric tables.
History of trigonometry: the emergence and development François Viète which were introduced in “Mathematical canon” (1579) provides a thorough and systematic, albeit unsubstantiated, characteristic plane and spherical trigonometry. But Albrecht Dürer was the same, thanks to whom the world was sinusoid.
The merits of Leonhard Euler
Providing modern trigonometry content and type of merit was Leonhard Euler. His treatise “Introduction to endless analysis” (1748) contains a definition of “trigonometric functions”, which is equivalent to today. Thus, the scientist could determine the inverse function. But that’s not all.
Definition of trigonometric functions on the entire real line was made possible by Euler’s research not only permissible negative angles, but the angles of over 360 °. He was first in his works proved that cosine and tangent right angle negative. Decomposition of entire stages cosine and sine was also the merit of the scientist. The general theory of trigonometric series and study the convergence of series were obtained objects of research Euler. However, working on issues related tasks, he made many discoveries in this area. It was through his work continued history of trigonometry. Briefly in his writings he touched on spherical trigonometry.

Applications of trigonometry
Trigonometry is not related to applied sciences, real everyday problem it is rarely used. However, this fact does not diminish its significance. It is important, for example, the technique of triangulation that allows astronomers to accurately measure the distance to stars minded and control the satellite navigation system.
Also trigonometry is used in navigation, music theory, acoustics, optics, analysis of financial markets, electronics, probability theory, statistics, biology, medicine (such as deciphering ultrasound ultrasound and computed tomography), pharmaceutics, chemistry, number theory, seysmolohyyy , meteorology, oceanography, cartography, many branches of physics, topography and geodesy, architecture, phonetics, economics, electronic engineering, mechanical engineering, computer graphics, and so krystallohrafyyy. d. The history of trigonometry and its role in the study of natural sciences and mathematics and studied day. Perhaps in the future areas of application will be more.
The history of the origin of basic concepts
The history of development of trigonometry and has more than one century. The introduction of the concepts that form the basis of this section of mathematical science, nor was momentary.
History of trigonometry: the emergence and development Thus, the term “sine” has a very long history. Mention of various segments of relationship triangles, circles found in scientific works, dating from the III century BC. The works of the great ancient scientists like Euclid, Archimedes, Apollo Perhskyy already containing the first study of these relationships. New discoveries demanded some terminological clarification. Thus, the Indian scientist Ariabhata gives chord name ‘Jiva’, which means “bow string”. When Arab mathematical texts were translated into Latin, the term was replaced by a value close sinuses (ie “bend”).
The word “cosine” appeared much later. This term is a shortened version of the Latin phrase “extra sine”.
The emergence of tangents associated with decoding the problem of determining the length of the shadow. The term “tangent” entered in the X century Arab mathematician Abul-Wafa, was the first table to determine tangents and kotanhensov. But European scientists were unaware of these developments. German mathematician and astronomer Rehymontan rediscovered these concepts in 1467 The proof of the theorem of tangents – to his credit. But the term is translated as “concerning”.