Trigonometric function is one of the basic elementary functions, which takes angle (the most commonly used radian system in mathematics, the same below) as the independent variable, and the coordinates of the intersection point between the terminal edge of any angle and the unit circle or its ratio as the dependent variable. The trigonometric function relates the internal angle of a right triangle to the ratio of its two sides, and can also be defined by the lengths of various line segments related to the unit circle equivalently. Trigonometric function plays an important role in studying the properties of geometric shapes such as triangles and circles, and is also a basic mathematical tool for studying periodic phenomena.

Chinese name

trigonometric function

Foreign name

trigonometric function

presenter

Indian mathematician

Show time

Fifth century A.D.

area of application

Function, image

Applied discipline

mathematics

Development history

origin

From the 5th century to12nd century, Indian mathematicians made great contributions to trigonometry. Although trigonometry was still a computing tool and an accessory of astronomy at that time, the content of trigonometry was greatly enriched through the efforts of Indian mathematicians.

The concepts of sine and cosine in trigonometry were first introduced by Indian mathematicians, who also made sine tables more accurate than Ptolemy.

As we already know, the chord table created by Ptolemy and Hipparchus is a circular full chord table, which corresponds to arcs and chords sandwiched between arcs. Unlike Indian mathematicians, they correspond the half chord (AC) to the half arc (AD) of the whole chord, that is, AC corresponds to ∠AOC. In this way, they created a sine table instead of a full chord table.

Indians call the chord (AB) connecting the two ends of the arc (AB) "jiba", which means bowstring; One half (AC) of AB is called "Al Hajiwa". Later, when the word "Jiwa" was translated into Arabic, it was misunderstood as "bend" and "concave", and Arabic was "dschaib". /kloc-in the 0/2nd century, Arabic was translated into Latin, and the word was translated into "dou".

Ancient Greek history

The early study of trigonometric functions can be traced back to ancient times. The founder of trigonometry in ancient Greece was Hippocius in the 2nd century BC. According to the practice of ancient Babylonians, he divided the circumference into 360 equal parts (that is, the radian of the circumference is 360 degrees, which is different from the modern arc system). For a given radian, he gives the corresponding chord length, which is equivalent to the modern sine function. Hipachas actually given the earliest numerical table of trigonometric functions. However, trigonometry in ancient Greece was basically spherical. This is related to the fact that the main body of ancient Greek research is astronomy. Menelaus described Menelaus theorem of spherical surface with sine in his book "The Science of Sphere". The application of trigonometry and astronomy in ancient Greece reached its peak in Ptolemy's time in Egypt. Ptolemy calculated the sine values of 36-degree angle and 72-degree angle in Syntaxis Mathematica, and gave the calculation methods of sum angle formula and half angle formula. Ptolemy also gave sine values corresponding to all integer radians and semi-integer radians from 0 to 180 degrees.