The History of Trigonometry refers to the development, across multiple ancient and medieval civilizations, of methods for relating angles and the lengths of sides in triangles, and of the functions (such as sine, cosine, and tangent) used to express those relationships. The field is generally treated as a cumulative tradition spanning Babylonian astronomy, Greek geometry, Indian and Islamic mathematics, and the eventual codification of modern trigonometric notation in early modern Europe. Some historians frame this as a single continuous tradition, while others emphasize independent or loosely connected origins in different regions; this is discussed briefly below and treated more fully on linked pages.

Historians broadly agree on several major milestones. Babylonian astronomers compiled tables of celestial observations that some scholars argue contain proto-trigonometric reasoning, though this interpretation is debated. The Greek astronomer Hipparchus of Nicaea (2nd century BCE) is often credited with producing the earliest known systematic table of chords, a precursor to the sine function, for use in astronomical calculations, though priority relative to earlier Babylonian work is disputed (see Controversies). This work was extended by later Greek astronomers, most notably Ptolemy in the *Almagest* (2nd century CE).

Independently, Indian mathematicians and astronomers, including Aryabhata (5th century CE), developed sine and versine tables and associated computational techniques. These methods were transmitted to and substantially developed within the Islamic world, where scholars such as al-Battani (9th-10th century CE) refined trigonometric methods for astronomical use, introduced or popularized additional trigonometric ratios, and helped systematize the discipline as a distinct branch of mathematics separate from astronomy. Other Islamic-era mathematicians, such as al-Khwarizmi, Abu al-Wafa, and Nasir al-Din al-Tusi, contributed tangent and cotangent functions and spherical trigonometry. These traditions were later transmitted to medieval Europe, where trigonometry was further formalized, particularly from the 16th century onward with the work of figures such as Regiomontanus and later Viète. A more detailed account of these developments appears on the history-of-trigonometry-history page.

There is scholarly debate over the degree to which these regional traditions developed independently versus through transmission and mutual influence, and over how much credit for specific innovations should be attributed to particular individuals versus their broader scholarly communities. These questions are noted briefly here and treated in full under Viewpoints and Controversies below.

There is broad consensus among historians of mathematics that trigonometry, as a systematic discipline, developed cumulatively across multiple civilizations rather than originating in a single time or place, and that Greek, Indian, and Islamic contributions were each substantive rather than merely transitional. See history-of-trigonometry-multi-civilizational-development-consensus.

• Diffusionist viewpoint - Emphasizes the transmission and synthesis of trigonometric knowledge across civilizations (Babylonian to Greek to Indian to Islamic to European), treating later developments as building substantially on inherited material. See history-of-trigonometry-diffusionist-viewpoint.
• Independent-origins viewpoint - Emphasizes that key innovations, particularly in India and the Islamic world, arose from independent problems (e.g., astronomical and calendrical needs) and reflect original contributions rather than mere elaboration of Greek sources. See history-of-trigonometry-independent-origins-viewpoint.
• Eurocentric-revisionist viewpoint - Holds that earlier historiography overstated Greek originality and underrepresented non-European contributions, and argues for revised attribution of certain foundational concepts (e.g., the sine function) to Indian and Islamic mathematicians. See history-of-trigonometry-eurocentric-revisionist-viewpoint.
• Traditionalist Greek-primacy viewpoint - Holds that the geometric framework established by Hipparchus and Ptolemy constitutes the conceptual foundation of trigonometry, with later traditions viewed primarily as extensions or computational refinements of that framework. See history-of-trigonometry-greek-primacy-viewpoint.

• Dispute over whether Hipparchus or earlier Babylonian astronomers should be credited with the first systematic angle-based astronomical tables. See history-of-trigonometry-hipparchus-babylonian-priority-controversy.
• Dispute over the attribution of the modern sine function's origin to Indian versus Greek sources. See history-of-trigonometry-sine-function-origin-controversy.

• History: history-of-trigonometry-history
• Debate: history-of-trigonometry-hipparchus-table-of-chords-accuracy-debate
• Viewpoint Debate: history-of-trigonometry-diffusionist-viewpoint-debate
• Consensus: history-of-trigonometry-multi-civilizational-development-consensus
• Controversy: history-of-trigonometry-sine-function-origin-controversy
• Related Main Topic: Hipparchus of Nicaea
• Related Main Topic: Al-Battani

1. Otto Neugebauer, *A History of Ancient Mathematical Astronomy* (Berlin: Springer-Verlag, 1975).
2. Glen Van Brummelen, *The Mathematics of the Heavens and the Earth: The Early History of Trigonometry* (Princeton: Princeton University Press, 2009).
3. J. L. Berggren, *Episodes in the Mathematics of Medieval Islam*, 2nd ed. (New York: Springer, 2003).
4. David Pingree, “The Recovery of Early Greek Astronomy from India,” *Journal for the History of Astronomy* 7 (1976): 109-123.
5. Kim Plofker, *Mathematics in India* (Princeton: Princeton University Press, 2009).