The knowledge points of trigonometric functions are:
The sine (sin), cosine (cos), tangent (tan), cotangent (cot) and secant (sec) of the acute angle A , cosecant (csc) are called acute trigonometric functions of angle A.
Sine (sin) is equal to the ratio of the opposite side to the hypotenuse; sinA=a/c.
Cosine (cos) is equal to the ratio of the adjacent side to the hypotenuse; cosA=b/c.
tangent (tan) is equal to the ratio of the opposite side to the adjacent side; tanA=a/b.
Cotangent (cot) is equal to the adjacent side compared to the opposite side; cotA=b/a.
Secant (sec) is equal to the ratio of the hypotenuse to the adjacent side; secA=c/b.
Cosecant (csc) is equal to the ratio of the hypotenuse to the opposite side. cscA=c/a.
The origin of trigonometric functions
From the fifth to the twelfth century AD, Indian mathematicians made great contributions to trigonometry. Although trigonometry was still a calculation tool and an accessory to astronomy at that time, the content of trigonometry was greatly enriched due to the efforts of Indian mathematicians.
The concepts of "sine" and "cosine" in trigonometry were first introduced by Indian mathematicians. They also created a more accurate sine table than Ptolemy.
We already know that the chord table created by Ptolemy and Hipparchus is a full chord table of a circle, which corresponds to the arcs of the arcs and the chords sandwiched by the arcs. Indian mathematicians are different. They correspond the half chord (AC) to half of the arc (AD) of the full chord, that is, AC corresponds to ∠AOC. In this way, what they create is no longer a "full chord table", but a "whole chord table". It's a "sine table".
The Indians call the string (AB) connecting the two ends of the arc (AB) "jiba", which means bow string; they call half of AB (AC) "alhajiba". Later, when the word "Jiva" was translated into Arabic, it was misunderstood as "bend" or "recess", and the Arabic word was "dschaib". In the twelfth century, when the Arabic was translated into Latin, the word was translated into "sinus".