History of trigonometry

Early study of triangles can be traced to the 2nd millennium BC, in Egyptian mathematics (Rhind Mathematical Papyrus) and Babylonian mathematics. Trigonometry was also prevalent in Kushite 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), who discovered the sine function. During the Middle Ages, the study of trigonometry continued in Islamic mathematics, by mathematicians such as Al-Khwarizmi and Abu al-Wafa. It became an independent discipline in the Islamic world, where all six trigonometric functions were known. Translations of Arabic and Greek texts led to trigonometry being adopted as a 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". The modern words "sine" and "cosine" are derived from the Latin word sinus via mistranslation from Arabic (see Sine and cosine#Etymology). Particularly Fibonacci's sinus rectus arcus proved influential in establishing the term. The word tangent comes from Latin tangens meaning "touching", since the line touches the circle of unit radius, whereas secant stems from Latin secans "cutting" since the line cuts the circle. The prefix "co-" (in "cosine", "cotangent", "cosecant") is found in Edmund Gunter's Canon triangulorum (1620), which defines the cosinus as an abbreviation for the sinus complementi (sine of the complementary angle) and proceeds to define the cotangens similarly. The words "minute" and "second" are derived from the Latin phrases partes minutae primae and partes minutae secundae.