sign / sine / syne are similar-sounding terms with different meanings (referred to as homophones). To better understand the differences, see below for definitions, pronunciation guides, and example sentences using each term. 👇
sign: (noun) a perceptible indication of something not immediately apparent (as a visible clue that something has happened). (noun) a public display of a message. (noun) (medicine) any objective evidence of the presence of a disorder or disease. (noun) a gesture that is part of a sign language. (noun) a fundamental linguistic unit linking a signifier to that which is signified; --de Saussure. (noun) a character indicating a relation between quantities. (verb) mark with one's signature; write one's name (on). (verb) approve and express assent, responsibility, or obligation. (verb) be engaged by a written agreement. (verb) engage by written agreement. (verb) communicate silently and non-verbally by signals or signs. (verb) place signs, as along a road. (verb) communicate in sign language.
sine: (noun) ratio of the length of the side opposite the given angle to the length of the hypotenuse of a right-angled triangle.
syne: NA
sign: s·AY·n
sine: s·AY·n
syne: NA
(Examples are Wikipedia snippets under the CC ShareAlike 3.0 license. Definitions drawn from WordNet.)