Before defining the circular functions, we equipped the cycle with four axes and a language to say in which “piece” of the loop a number is. Then we study the property that all these functions will have in common: periodicity. The story The word sine has a curious history. Fifth-century Indian astronomers such as Aryabhata tabulated the half-chord, which they called jya-ardha or simply jya. Arabic translators transcribed the term as jiba, written only with consonants, jb. In the 12th century, Latin translators read jaib — “fold,” “breast” — and translated it as sinus. The tangent and secant gained their name from the Danish Thomas Fincke, in 1583, and the prefix co- of cosine, cotangent and cosecant, which means “of the complement”, was fixed by Edmund Gunter in 1620.