sinical adj.

one of the three fundamental functions of trigonometry,  1590s (in Thomas Fale's "Horologiographia, the Art of Dialling"), from Latin sinus "fold in a garment, bend, curve, bosom" (see sinus). The Latin word was used mid-12c. by Gherardo of Cremona's Medieval Latin translation of Arabic geometrical texts to render Arabic jiba "chord of an arc, sine" (from Sanskrit jya "bowstring"), which he confused with jaib "bundle, bosom, fold in a garment." The engineering sine wave is attested from 1915.

compound adjectival word-forming element, usually interchangeable with -ic but sometimes with specialized sense (such as historic/historical, politic/political), Middle English, from Late Latin -icalis, from Latin -icus + -alis (see -al (1)). Probably it was needed because the forms in -ic often took on a noun sense (for example physic). Forms in -ical tend to be attested earlier in English than their twins in -ic.