The words sign, sine, syne sound the same but have different meanings and spellings. Why do sign, sine, syne sound the same even though they are completely different words?
The answer is simple: sign, sine, syne are homophones of the English language.
Something that suggests the presence or existence of a fact, condition, or quality.
An act or gesture used to convey an idea, a desire, information, or a command: gave the go-ahead sign.
Sign language.
A displayed structure bearing lettering or symbols, used to identify or advertise a place of business: a motel with a flashing neon sign outside.
The ordinate of the endpoint of an arc of a unit circle centered at the origin of a Cartesian coordinate system, the arc being of length x and measured counterclockwise from the point (1, 0) if x is positive or clockwise if x is negative.
In a right triangle, the ratio of the length of the side opposite an acute angle to the length of the hypotenuse.
Afterward; since then; since.
Thereupon; next.
Since.
Before now; ago.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.
If they are spelled the same then they are also homographs (and homonyms); if they are spelled differently then they are also heterographs (literally "different writing").