History of trigonometry

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. 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 trigōnon, "triangle" and metron, "measure".

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 loaned into Arabic as jiba. This term was then transformed into the genuine Arabic word jayb, 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. Particularly Fibonacci's sinus rectus arcus proved influential in establishing the term sinus. The words "minute" and "second" are derived from the Latin phrases partes minutae primae and partes minutae secundae. These roughly translate to "first small parts" and "second small parts".

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