cosinus

Cosine is a contraction of Latin complementi sinus — 'sine of the complement.' The cosine of an angle is equal to the sine of the complementary angle (90° minus the given angle). English mathematician Edmund Gunter coined the abbreviation co.sinus in 1620, and it was quickly shortened to cosinus in Latin and then cosine in English. The word is a compound: co- from Latin complementum (that which fills up, completes), and sine from Latin sinus (fold, bay, bosom). The word sine itself has one of mathematics's stranger etymology stories — it is a mistranslation of an Arabic word that was itself a transliteration of a Sanskrit term, with the Arabic sense lost along the way.

The Sanskrit word jīvā (originally meaning a bowstring) was used by Indian mathematicians to name what we now call the sine — the half-chord of a doubled arc in a circle. When Arabic scholars translated Indian astronomical texts, they transliterated jīvā as jiba, a word with no meaning in Arabic. Medieval European translators, encountering the written form jb (Arabic omits most short vowels in writing), misread it as jaib, an Arabic word meaning 'fold, pocket, bosom.' They translated jaib into Latin as sinus — the Latin word for 'fold, bay, or bosom.' From that mistranslation, every trigonometric term in European mathematics descends. The sine, the cosine, the cosecant — all carry in their name a pocket that exists only because of a scribal error in medieval Toledo.

The systematic development of the six trigonometric functions — sine, cosine, tangent, cotangent, secant, cosecant — was largely the achievement of Islamic astronomers and mathematicians from the ninth through the thirteenth centuries. Al-Battani, Abu al-Wafa, and Nasir al-Din al-Tusi extended the Greek chord-based trigonometry into the ratio-based system that European mathematicians inherited through Latin translation. The 'co-' prefix functions that Gunter formalized in 1620 — cosine, cotangent, cosecant — had been implicit in Islamic trigonometry for centuries before they received standardized Latin names.

Today cosine is inseparable from signal processing, wave physics, and Fourier analysis. The cosine function describes the oscillation of any wave-like phenomenon: sound, light, radio signals, electrical current. The Fourier transform — which decomposes any signal into a sum of sines and cosines — underlies every digital audio format, every image compression algorithm, and every wireless communication system. Edmund Gunter's 1620 abbreviation, carrying the memory of a Sanskrit bowstring and a medieval scribal error, is now executed billions of times per second inside the devices in every pocket in the world.