cosin

Cosin is a term that may refer to the cosine function in trigonometry when encountered in nonstandard spellings, misspellings, or as an informal abbreviation. In many languages the corresponding term is cosinus or coseno, while cosin itself is not the standard English designation for the function.

Mathematically, the cosine of an angle θ, denoted cos θ, can be defined in several equivalent ways: as the x-coordinate of a point on the unit circle, as the ratio of the adjacent side to the hypotenuse in a right triangle, and via its Maclaurin series cos θ = 1 − θ^2/2! + θ^4/4! − ... . The cosine function is even, periodic with period 2π, and its range is [−1, 1].

Key identities include sin^2 θ + cos^2 θ = 1 and the angle addition formulas cos(α+β) = cos α cos β − sin α sin β. In calculus, d/dθ cos θ = −sin θ, and ∫ cos θ dθ = sin θ + C. The function also plays a central role in Fourier analysis, oscillations, and signal processing.

Cosin can also occur as a proper noun, used as a surname or place or organization name independent of the mathematical concept. When encountered, the intended meaning depends on context and may be orthogonal to trigonometry.

See also: cosine, sine, trigonometry, unit circle, cosinus.