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History of trigonometry

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Early study of triangles can be traced to Egyptian mathematics (Rhind Mathematical Papyrus) and Babylonian mathematics during the 2nd millennium BC. Systematic study of trigonometric functions began in Hellenistic mathematics, reaching India as part of Hellenistic astronomy.

Sine and cosineSine and cosineIn mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse.Indian mathematicsIndian mathematicsDevelopment of mathematics in South AsiaThe tradition of Indian mathematics flourished in South Asia from circa 1200 BCE until the late 18th century, when it merged into a global discipline. Important contributions were made throughout its history, but especially during its classical period (400 CE to 1200 CE) by scholars such as Aryabhata, Brahmagupta, Bhaskara II, Virasena, Mahaviracharya and Varāhamihira.Babylonian mathematicsBabylonian mathematicsBabylonian mathematics (also known as Assyro-Babylonian mathematics) is the mathematics developed or practiced by the people of Mesopotamia, as attested by sources surviving mainly from the Old Babylonian period (1830–1531 BC) to the Seleucid period from the last three or four centuries BC. With respect to content, there is scarcely any difference between the two groups of texts. Babylonian mathematics remained constant, in character and content, for over a millennium.Indian astronomyIndian astronomyAstronomy has a long history in the Indian subcontinent, stretching from pre-historic to modern times. Some of the earliest roots of Indian astronomy can be dated to the period of Indus Valley Civilisation or earlier. Astronomy later developed as a discipline of Vedanga, or one of the "auxiliary disciplines" associated with the study of the Vedas dating 1500 BCE or older.AryabhataAryabhataAryabhata (Sanskrit: आर्यभट, IAST: Āryabhaṭa) or Aryabhata I (476–550 CE) was the first of the major mathematician-astronomers and early physicist from the classical age of Indian mathematics and Indian astronomy. His works include the Āryabhaṭīya (which mentions that in 3600 Kali Yuga, 499 CE, he was 23 years old) and the Arya-siddhanta.Rhind Mathematical PapyrusRhind Mathematical PapyrusAncient Egyptian mathematical documentThe Rhind Mathematical Papyrus (RMP; also designated as papyrus British Museum 10057, pBM 10058, and Brooklyn Museum 37.1784Ea-b) is one of the best known examples of ancient Egyptian mathematics. It is one of two well-known mathematical papyri, along with the Moscow Mathematical Papyrus. The Rhind Papyrus is the larger, but younger, of the two.Ancient Greek mathematicsAncient Greek mathematicsAncient Greek mathematics refers to the history of mathematical ideas and texts in Ancient Greece during classical and late antiquity, mostly from the 5th century BC to the 6th century AD. Greek mathematicians lived in cities spread around the shores of the ancient , from Anatolia to Italy and North Africa, but were united by Greek culture and the Greek language.TrigonometryTrigonometryTrigonometry (from Ancient Greek τρίγωνον (trígōnon) 'triangle' and μέτρον (métron) 'measure') is a branch of mathematics concerned with relationships between angles and side lengths of triangles. In particular, the trigonometric functions relate the angles of a right triangle with ratios of its side lengths. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.Mathematics in the medieval Islamic worldMathematics in the medieval Islamic worldMathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built upon syntheses of Greek mathematics (Euclid, Archimedes, Apollonius) and Indian mathematics (Aryabhata, Brahmagupta). Important developments of the period include extension of the place-value system to include decimal fractions, the systematised study of algebra and advances in geometry and trigonometry.Ancient Egyptian mathematicsAncient Egyptian mathematicsAncient Egyptian mathematics is the mathematics that was developed and used in Ancient Egyptc. 3000 to c. 300 BCE, from the Old Kingdom of Egypt until roughly the beginning of Hellenistic Egypt. The ancient Egyptians utilized a numeral system for counting and solving written mathematical problems, often involving multiplication and fractions. Evidence for Egyptian mathematics is limited to a scarce amount of surviving sources written on papyrus.IndiaIndiaCountry in South AsiaIndia, officially the Republic of India, is a country in South Asia. It is the world's seventh-largest country by area and the largest by population. Bounded by the Indian Ocean on the south, the Arabian Sea on the southwest, and the Bay of Bengal on the southeast, it shares land borders with Pakistan to the west; China, Nepal, and Bhutan to the north; and Bangladesh and Myanmar to the east. In the Indian Ocean, India is near Sri Lanka and the Maldives.Middle AgesMiddle AgesA medieval stained glass panel from Canterbury Cathedral, c. 1175 – c. 1180, depicting the Parable of the Sower, a biblical narrativeDurationc.Ancient Greek astronomyAncient Greek astronomyAncient Greek astronomy is the astronomy written in the Greek language during classical antiquity. Greek astronomy is understood to include the Ancient Greek, Hellenistic, Greco-Roman, and late antique eras.τρίγωνοντρίγωνονRelated word or term.μέτρονμέτρονRelated word or term.

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