arccosv

Arccosv is a term used in some programming and mathematical contexts to denote the arccosine operation applied element-wise to a vector, or more generally, the arccos of a scalar and the vectorized extension of that operation. In this sense, arccosv(v) returns a vector where each component is the arccos of the corresponding component of v. For a scalar input, arccosv(s) reduces to the ordinary arccos function.

In practice, arccosv is defined for inputs whose components lie within the domain of the arccos function, typically [-1, 1]. For each component x_i in a vector x, the value arccosv(x)_i = arccos(x_i). The resulting components usually lie in the range [0, π] when the input is measured in radians; if degrees are used, the range is [0, 180]. When any component lies outside [-1, 1], the result is undefined or yields a domain error or NaN, depending on the implementation.

Arccosv inherits properties from the arccos function, applied element-wise. The function is decreasing on its domain, and cos(arccos(x)) equals x for x in [-1, 1]. The derivative of arccos with respect to its argument is -1 / sqrt(1 - x^2), a relation that extends to each component in a vector input. In software libraries, arccosv may be implemented as a scalar arccos applied to each element of a vector, or as an alias of existing vectorized arccos functions (such as acos for scalar and vec types), depending on naming conventions.

Common uses include vectorized transformations in graphics, data normalization, and coordinate conversions where per-component inverse cosine operations are required. See also arccos, inverse trigonometric functions, and vectorized math.