Math World: Trigonometry

What is trigonometry?

Introduction of trigonometry?

Trigonometry was developed by ancient Egyptians, Babylonians, and Greeks over three thousand years ago. They used it to find the lengths of the sides of triangle and the measure of the angles. In Egypt, trigonometry was used to establish land boundaries after the annual flood of the Nile river. Today it is used in electronics, surveying and other areas in engineering, and is a vital tool for further courses in mathematics, such as calculus.

History of trigonnmetry

Early study of triangles can be traced to the 2nd millennium BC, in Egyptian mathematics (Rhind Mathematical Papyrus) and Babylonian mathematics. Systematic study of trigonometric functions began in Hellenistic mathematics, reaching India as part of Hellenistic astronomy.^[1] In Indian astronomy, the study of trigonometric functions flourished in the Gupta period, especially due to Aryabhata (sixth century CE). During the Middle Ages, the study of trigonometry continued in Islamic mathematics, hence it was adopted as a separate subject in the Latin West beginning in the Renaissance with Regiomontanus. The development of modern trigonometry shifted during the western Age of Enlightenment, beginning with 17th-century mathematics (Isaac Newton and James Stirling) and reaching its modern form with Leonhard Euler (1748).

The term "trigonometry" was derived from Greek τρίγωνον trigōnon, "triangle" and μέτρον metron, "measure".^[2]

Our modern word "sine" is derived from the Latin word sinus, which means "bay", "bosom" or "fold", translating Arabic jayb. The Arabic term is in origin a corruption of Sanskrit jīvā, or "chord". Sanskrit jīvā in learned usage was a synonym of jyā "chord", originally the term for "bow-string". Sanskrit jīvā was rendered into Arabic as jiba.^[3][4] This term was then transformed into the genuine Arabic word jayb,^[4] meaning "bosom, fold, bay", either by the Arabs or by a mistake of the European translators such as Robert of Chester (perhaps because the words were written without vowels), who translated jayb into Latin as sinus.^[3]Particularly Fibonacci's sinus rectus arcus proved influential in establishing the term sinus.^[5] The words "minute" and "second" are derived from the Latin phrases partes minutae primae and partes minutae secundae.^[6] These roughly translate to "first small parts" and "second small parts".