the exponential series. He presented "Euler's formula", as well as near-modern abbreviations (sin., cos., tang., cot., sec., and cosec.). A few functions were common historically, but are now seldom used, such as the chord, the versine (which appeared in the earliest tables), the coversine, the haversine, the exsecant and the excosecant. The list of trigonometric identities shows more relations between these functions. Etymology The word derives from Latin sinus, meaning "bend; bay", and more specifically "the hanging fold of the upper part of a toga", "the bosom of a garment", which was chosen as the translation of what was interpreted as the Arabic word jaib, meaning "pocket" or "fold" in the twelfth-century translations of works by Al-Battani and al-Khwārizmī into Medieval Latin. The choice was based on a misreading of the Arabic written form j-y-b (), which itself originated as a transliteration from Sanskrit , which along with its synonym (the standard Sanskrit term for the sine) translates to "bowstring", being in turn adopted from Ancient Greek "string". 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. See also All Students Take Calculus – a mnemonic for recalling the signs of trigonometric functions in a particular quadrant of a Cartesian plane Bhaskara I's sine approximation formula Small-angle approximation Differentiation of trigonometric functions Generalized trigonometry Generating trigonometric tables Hyperbolic function List of integrals of trigonometric functions List of periodic functions List of trigonometric identities Polar sine – a generalization to vertex angles Proofs of trigonometric identities Versine – for several less used trigonometric functions Notes References Lars Ahlfors, Complex Analysis: an introduction to the theory of analytic functions of one complex variable, second edition, McGraw-Hill Book Company, New York, 1966. Boyer, Carl B., A History of Mathematics, John Wiley & Sons, Inc., 2nd edition. (1991). . Gal, Shmuel and Bachelis, Boris. An accurate elementary mathematical library for the IEEE floating point standard, ACM Transactions on Mathematical Software (1991). Joseph, George G., The Crest of the Peacock: Non-European Roots of Mathematics, 2nd ed. Penguin Books, London. (2000). . Kantabutra, Vitit, "On hardware for computing