The chord of an angle subtends the arc of the angle.Īncient Greek and Hellenistic mathematicians made use of the chord. In other words, the quantity he found for the seked is the cotangent of the angle to the base of the pyramid and its face. 'If a pyramid is 250 cubits high and the side of its base 360 cubits long, what is its seked?'Īhmes' solution to the problem is the ratio of half the side of the base of the pyramid to its height, or the run-to-rise ratio of its face. 1680–1620 BC), contains the following problem related to trigonometry: The Rhind Mathematical Papyrus, written by the Egyptian scribe Ahmes (c. The Egyptians, on the other hand, used a primitive form of trigonometry for building pyramids in the 2nd millennium BC. There is, however, much debate as to whether it is a table of Pythagorean triples, a solution of quadratic equations, or a trigonometric table. 1900 BC), some have even asserted that the ancient Babylonians had a table of secants but does not work in this context as without using circles and angles in the situation modern trigonometric notations won't apply.

Based on one interpretation of the Plimpton 322 cuneiform tablet (c. The Babylonian astronomers kept detailed records on the rising and setting of stars, the motion of the planets, and the solar and lunar eclipses, all of which required familiarity with angular distances measured on the celestial sphere.

However, as pre-Hellenic societies lacked the concept of an angle measure, they were limited to studying the sides of triangles instead. The ancient Egyptians and Babylonians had known of theorems on the ratios of the sides of similar triangles for many centuries. These roughly translate to 'first small parts' and 'second small parts'.ĭevelopment Ancient Near East The words 'minute' and 'second' are derived from the Latin phrases partes minutae primae and partes minutae secundae. Particularly Fibonacci's sinus rectus arcus proved influential in establishing the term sinus. This was then interpreted as 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, who translated jayb into Latin as sinus. Sanskrit jīvā was rendered (adopted) into Arabic as jiba, written jb جب. The sine function was later also adapted in the variant jīvā. Its synonyms are jivā, siñjini, maurvi, guna, etc. The Hindus defined these as functions of an arc of a circle, not of an angle, hence their association with a bow string, and hence the 'chord of an arc' for the arc is called 'a bow' (dhanu, cāpa). The Hindu term for sine in Sanskrit is jyā 'bow-string', the Hindus originally introduced and usually employed three trigonometric functions jyā, koti-jyā, and utkrama-jyā. Is indirectly, via Indian, Persian and Arabic transmission, derived from the Greek term khordḗ 'bow-string, chord'. The modern word 'sine' is derived from the Latin word sinus, which means 'bay', 'bosom' or 'fold' The term 'trigonometry' was derived from Greek τρίγωνον trigōnon, 'triangle' and μέτρον metron, 'measure'. 2.6 European renaissance and afterwards.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). Translations of Arabic and Greek texts led to trigonometry being adopted as a subject in the Latin West beginning in the Renaissance with Regiomontanus. It became an independent discipline in the Islamic world, where all six trigonometric functions were known. During the Middle Ages, the study of trigonometry continued in Islamic mathematics, by mathematicians such as Al-Khwarizmi and Abu al-Wafa. In Indian astronomy, the study of trigonometric functions flourished in the Gupta period, especially due to Aryabhata (sixth century CE), who discovered the sine function. Systematic study of trigonometric functions began in Hellenistic mathematics, reaching India as part of Hellenistic astronomy.

Trigonometry was also prevalent in Kushite mathematics. Early study of triangles can be traced to the 2nd millennium BC, in Egyptian mathematics ( Rhind Mathematical Papyrus) and Babylonian mathematics.

162 in babylonian numerals