Positive: the side that is directly opposite, the side that is opposite to the angle
Excess: redundant, secondary, other than "positive"
Tangential: Close, close, derived from the relationship between arcs and straight lines
The word sine originated from the Arab Rechio Montan. He was a leading figure in Western European mathematics in the fifteenth century. His book "On Various Triangles", completed in 1464, was published in 1533. This is a book on pure trigonometry, which separated trigonometry from astronomy and became an independent discipline. Mathematics branch.
Cosine (cosine) and cotangent (cotangent) were first used by the Englishman Genger. They first appeared in his "Artillery Surveying" published in London in 1620.
Secant (secant) and tangent (tangent) were invented by the Danish mathematician Thomas Fink and were first seen in his book "Circle Geometry".
The word cosecant was coined by Riticus. It was first seen in his book "Court Music" published in 1596.
In 1626, Albert Grod first introduced the abbreviated triangular symbols: "sin", "tan", and "sec". In 1675, the Englishman Ocutt first introduced the remaining abbreviated triangle symbols: "cos", "cot", and "csc". But it was not until 1748, after the mathematician Euler quoted it, that it gradually became common.
Since 1949, due to the influence of the textbooks of the former Soviet Union, "cot" in Chinese mathematics books has been changed to "ctg"; "tan" has been changed to "tg", and the other four symbols have remained unchanged. This is why the popular imported functional calculators on the Chinese market have "tan" buttons but no "tg" buttons.