Trigonometric function (also called "circular function") is a function of angle; They are very important in studying triangles, simulating periodic phenomena and many other applications. Trigonometric function is usually defined as the ratio of two sides of a right triangle containing this angle, and it can also be equivalently defined as the lengths of various line segments on the unit circle.
Trigonometric functions include sine, cosine, tangent and cotangent, and the corresponding sides are: sine is the opposite side of hypotenuse; Cosine is the ratio of adjacent side to hypotenuse; The tangent is the opposite side of the adjacent side; Cotangent is the comparison of adjacent edges.
trigonometric function
The birth of trigonometric function stems from people's demand for "measurement technology". The ancient Greek astronomer Hipparchus (c. 190 _ c. 120) made the first "astronomical watch" in human history, also known as the founder of trigonometry, in order to measure the angle and distance on the celestial sphere.
The so-called "chord" is the connecting line between two points on a circle (more generally, it can also refer to the connecting line between two points on an arbitrary curve), as shown in figure 1. Let ∠AOB=α be the central angle on the circle, and AB be the chord length corresponding to the central angle.
In the 4th-5th century A.D., trigonometry got a very important development in India. In an astronomical book called Siddhartha (translated as Siddhartha, literally meaning "established opinions, doctrines, axioms or recognized truths"), the definition of sine was correctly given. Then, Indian mathematician and astronomer Aryabhatiya (AD 476-550) took jya as sine, kojya as cosine cos, utkrama-jya as positive vector (1 minus cosine of a certain angle, that is, 1-cosθ), and otkramjya as sine.
In the 9th century, Mu _ ammdibnm sā al-khwā rizmā, c. _ 780 _ c.850, an Arab-Persian mathematician and astronomer, made the tangent table for the first time. Malva (766-869) gave cotangent, and applied sine, cosine, tangent and cotangent completely. Albategnius (C.858 _ 929) discovered secant (sec) and cosecant (csc) functions, and made the first cosecant table of every degree from 1 to 90. At this point, all six trigonometric functions are available, and the interoperability between trigonometric functions (such as sum and difference multiplication, multiplication and difference) is also available.