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.
Common trigonometric functions are sine function (SinX), declaration function (Cosx) and tangent function (tanx). Other trigonometric functions, such as cotangent function, secant function, cotangent function, vector function, semi-vector function, etc., are also applied in navigation, surveying, engineering and other disciplines. The relationship between different trigonometric functions can be obtained by geometric intuition or calculation, which is called trigonometric identity.
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.