cospi

Cospi is a shorthand mathematical and programming term for the function defined by cospi(x) = cos(pi * x). It is used in several programming languages and mathematical libraries as a convenient way to compute the cosine of a quantity expressed in units of pi, and to help manage numerical accuracy when the input is near multiples of pi.

For real x, cospi(x) takes values in the interval [-1, 1]. It is an even function, meaning cospi(-x) = cospi(x). It has a period of 2, so cospi(x + 2) = cospi(x). At integer arguments, cospi(n) = cos(pi n) = (-1)^n. It vanishes at half-integers, specifically at x = k + 1/2 for any integer k.

Implementation and use vary by language. In languages such as Julia, cospi (and related sinpi) are built-in functions that compute cos(pi*x) directly, often with argument-reduction strategies designed to maintain precision when x is near integers or half-integers. Other languages and math libraries provide analogous functionality under the same or similar naming conventions, or through simple definitions as cos(pi*x). The function is typically used in numerical analysis, computer graphics, signal processing, and any domain where quantities are naturally expressed in units of pi.

See also: cos, sin, pi, sinpi, tanpi.