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Trigonometry
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Trigonometry


TRIGONOMETRY is a branch of mathematics that studies trigonometric functions and their application in solving problems, mainly geometric ones. The word "trigonometry" is literally translated from Greek as "triangle + measurement" ..

The main task of trigonometry

The main task of trigonometry is the solution of triangles, that is finding unknown quantities of a triangle in terms of its known values. Any geometric problem can be reduced to a solution with the help of triangles, so trigonometry is applicable in planimetry (the study of plane geometric figures), and in stereometry (the study of spatial geometric figures).

Any trigonometric quantity is a function of the angle (varies with the angle), so the name "trigonometric functions" appeared.
Trigonometric functions are functions of the angle: sinus, cosine, tangent, cotangent, sec, and cosec.

Inverse trigonometric functions, or circular functions, are arcsine (arcsin), arccosine (arccos), arctangent (arctg), and arccotangent (arcctg).

Direct functions of the angle are used when the angle is found in the angle, and the inverse functions are used to find the angle.

History of trigonometry


The solution of the triangles was for a long time one of the sections of astronomy. But the rudiments of science can be found in the mathematical manuscripts of Ancient Egypt, China and Babylon. It is believed that the measurement of angles in degrees, minutes and seconds came to us from the Babylonian mathematicians.

The methods for solving spherical triangles were first written in writing by the Greek astronomer Hipparchus in the middle of the 2nd century BC.

The solutions of the triangles by Hipparchus and Ptolemy (the creator of the geocentric system of the world that dominated Copernicus) did not know sinuses, cosines and tangents. Sine and cosine lines began to be used by Indian astronomers (IV-V century). Later, trigonometry developed Arabic-speaking scientists (Muhammad from Bujan, Nasir ed-Din of Tus).

Europeans got acquainted with trigonometry in the 12th century. The outstanding German astronomer Regiomontan compiled the sine tables to within the seventh significant digit with an interval of 1 '.

The term "trigonometry" first appeared in 1595 as the title of the book of the German mathematician Bartholomeus Pitiscus (1561-1613).
The letter designations appeared in trigonometry only in the middle of the 18th century.




 Diagonals of a trapezoid | Описание курса | Sine