History of trigonometry
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| Laws and theorems |
| Calculus |
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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. In Indian astronomy, the study of trigonometric functions flourished in the Gupta period, especially due to Aryabhata (6th century AD), who discovered the sine function, cosine function, and versine function.
During the Middle Ages, the study of trigonometry continued in Islamic mathematics, building on earlier foundations from Indian (notably Aryabhata's sine and cosine concepts) and Greek (Hipparchus' chord table) sources. Mathematicians such as al-Khwarizmi and Abu al-Wafa made important contributions, but the field was fundamentally transformed by Nasir al-Din al-Tusi (1201–1274).
Al-Tusi was the first to treat trigonometry as an independent mathematical discipline, separate from astronomy. He fully established all six trigonometric functions (sine, cosine, tangent, cotangent, secant, cosecant) with complete proofs, and formulated the plane and spherical law of sines, the form still taught in schools and universities today. He also rewrote and corrected Ptolemy's Almagest, replacing chords with sine and tangent tables and adding practical, real-world examples.
Through translations of Arabic and Greek texts, this knowledge reached the Latin West. However, during the Renaissance, Regiomontanus (c. 1464) translated al-Tusi's work into Latin without crediting him, effectively erasing al-Tusi's name from European historiography. Consequently, for centuries, European textbooks mistakenly attributed the development of trigonometry to Regiomontanus and earlier Greek sources, sidelining al-Tusi's central role.
Modern scholarship has since restored al-Tusi's credit: he is now recognized in academic literature as the "Master of Trigonometry" the one who gave the field its modern, independent form.
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).