kosine

Kosine is not a standard mathematical term in most contexts. It is commonly encountered as a misspelling or transliteration variant of the trigonometric function cosine. In formal mathematical writing, the conventional spelling is cosine, often abbreviated cos. The form kosine may appear in OCR output, informal notes, or in texts that reflect nonstandard transliterations.

In mathematics, the cosine of an angle is defined as the ratio of the length of the adjacent side to the hypotenuse in a right triangle. Equivalently, it is the x-coordinate of the point on the unit circle corresponding to that angle. For real angles, cosine values lie in the interval [-1, 1] and the function is periodic with period 2π. It is an even function, meaning cos(−θ) = cos(θ). The Maclaurin series for cosine is cos x = 1 − x^2/2! + x^4/4! − ...

Cosine appears across many fields, including physics, engineering, computer science, and signal processing. In programming and numerical software, the standard function is typically written as cos(x); misspellings like kosine can lead to errors or undefined behavior in code. In some languages, related terms are cosinus or kosinus, reflecting regional spelling conventions rather than a separate function.

Beyond its mathematical definition, kosine as a term may also be found as a proper noun in branding, product names, or fictional works, where it does not carry a distinct mathematical meaning. When encountered, context usually clarifies whether it refers to the standard cosine function or to a nonstandard spelling.

See also: cosine, trigonometric functions, unit circle.