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The history of trigonometry spans millennia, from its early roots in astronomical calculations to its modern applications across sciences and engineering. This article traces the evolution of trigonometric concepts and methods, highlighting key contributions from civilizations such as the Babylonians, Greeks, Indians, and Islamic scholars, as well as later European developments. For a comprehensive overview of trigonometry itself, see Trigonometry. For debates on specific interpretations of historical contributions, refer to the Aryabhata - Mathematics - Consensus page.

This article covers the history of trigonometry from ancient times to modern developments. For an in-depth explanation of trigonometric concepts and their applications, see the main Trigonometry page. The Aryabhata - Mathematics - Consensus discusses debates surrounding Aryabhata's contributions.

The origins of trigonometry lie in ancient civilizations' need to solve practical problems in astronomy and construction. The Babylonians (circa 1800 BCE) developed a sexagesimal numeral system, which influenced later trigonometric tables. Their use of 360 degrees for a circle persisted as a standard convention.

Hipparchus of Rhodes (2nd century BCE) is credited with creating the first significant trigonometric table-the chord table-which listed chords in a unit circle for various angles. This work, though lost, was later referenced by Ptolemy. Hipparchus's methods were foundational for calculating astronomical positions.

Ptolemy's *Almagest* (2nd century CE) systematically compiled and expanded trigonometric knowledge, introducing the concept of the sine function indirectly through chords. His work bridged ancient Greek astronomy with later Islamic and Indian mathematics Toomer-G-J-Ptolemys-Almagest-1984.

In India, Aryabhata (5th-6th century CE) advanced trigonometry by providing early definitions of sine (*jiva*) and cosine (*kotijiva*), though his formulations differed from modern ones. His *Aryabhatiya* included tables for calculating these functions Plofker-Kim-Mathematics-in-India-2008.

During the Islamic Golden Age, scholars refined trigonometry into a more familiar form. Omar Khayyam (11th-12th century) contributed to the accuracy of trigonometric tables by addressing errors in prior works. Al-Kashi (14th-15th century) improved decimal-based calculations and compiled extensive trigonometric tables Berggren-J-Lennart-Episodes-in-the-Mathematics-of-Medieval-Islam-1986.

The 16th-century astronomer Nicolaus Copernicus applied trigonometry to his heliocentric model, using it to calculate planetary motions. Meanwhile, François Viète's *Canon Mathematicus seu ad Triangula* (1579) made systematic use of all six trigonometric functions for computing plane and spherical triangles.

Leonhard Euler (18th century) deepened the connection between trigonometry and complex analysis through his formula \( e^{ix} = \cos x + i \sin x \), unifying exponential and periodic functions Boyer-Carl-B-A-History-of-Mathematics-1985.

The development of logarithms by John Napier (1614) and Henry Briggs (17th century) revolutionized trigonometric calculations, enabling astronomers and surveyors to simplify complex multiplications into additions.

In the 19th and 20th centuries, Joseph Fourier's series extended trigonometric functions to analyze periodic phenomena like heat flow and sound waves. Lagrange's work on trigonometric interpolation further demonstrated their versatility in mathematics.

The mid-20th century saw computational advancements with digital calculators and software, making trigonometric functions widely accessible for engineering, physics, and computer graphics applications.

Some historians argue that the naming of sine (*sinus*) stems directly from a mistranslation of the Arabic term *jiba*, obscuring its Indian origins Sine-and-Cosine-Naming-Conventions-Controversy.

* Trigonometry * Aryabhata - Mathematics - Consensus * History-of-Mathematics-viewpoint * Sine-and-Cosine-Naming-Conventions * Debate-on-non-Western-contributions-to-trigonometry

1. Toomer, G.J., *Ptolemy's Almagest*, 1984. 2. Plofker, Kim, *Mathematics in India*, 2008. 3. Boyer, Carl B., *A History of Mathematics*, 1985. 4. Berggren, J. Lennart, *Episodes in the Mathematics of Medieval Islam*, 1986.