The essence of trigonometric function is the mapping between any set of angles and a set of ratio variables. The usual trigonometric function is defined in a plane rectangular coordinate system. Its definition field is the whole real number field. The other is defined in a right triangle, but it is incomplete. Modern mathematics describes them as the limit of infinite sequence and the solution of differential equation, and extends their definitions to complex system.

The origin of trigonometric function:

Sine (sine) originated from Arab Requio Montan. He was a leading figure in mathematics in western Europe in the15th century. His book Various Triangles was completed in 1464 and published in 1533. This book is a pure trigonometry, which breaks away from astronomy and becomes an independent branch of mathematics.

Cosine and cotangent were first used by an Englishman, Genzil, and first appeared in his "Artillery Investigation" published in London in 1620.

Secant (secant) and tangent (tangent) were first created by Danish mathematician Thomas Fink, and first appeared in his book Geometry of Circle.

Cotangent was created by Retius. It was first seen in the book "Palace Music" published by him 1596. In 1626, Abelt Glaude first introduced the abbreviated triangle symbols: "sin", "tan" and "sec".

1675, the British Orkut first introduced the remaining abbreviated triangle symbols: "cos", "cot" and "csc". But it was not until 1748 was quoted by the mathematician Euler that it gradually became universal.

From 1949, due to the influence of textbooks of the former Soviet Union, the word "cot" in China's mathematics books was changed to "CTG"; "Tan" was changed to "tg", and the other four symbols remained unchanged. This is why there is a "tan" key instead of "tg" key on the popular imported function calculator in China.

Refer to the above? Baidu encyclopedia-trigonometric function