Early study of trigonometry began with the ancient Egyptians and Babylonians studying properties of triangles in the 2nd millennium BC. This study continued and advanced in Hellenistic Greece and India, where systematic study of trigonometric functions began. During the Middle Ages, Islamic mathematicians adopted trigonometry as a separate subject and it spread to Western Europe in the Renaissance. Modern trigonometry developed further during the 17th-18th centuries with key contributions from mathematicians like Newton, Stirling, and Euler.

1. HISTORY OF TRIGNOMETRY

2. 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).

3. The term "trigonometry" was derived from the Greek word
"τριγωνομετρία" ("trigonometria"), meaning "triangle measuring", from
"τρίγωνο" (triangle) plus "μετρεῖν" (to 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.[clarification needed] 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[1]), 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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