arccos05

Arccos05 is not a standard term in mathematics. In most contexts, it would be read as arccos(0.5), the inverse cosine of the number 0.5. The arccos function, denoted arccos or its equivalent arc cos, selects the principal angle θ in radians (or degrees) whose cosine equals the given input.

The arccos function has a domain of [-1, 1], and its principal value lies in the interval [0, π] radians (0 to 180 degrees). For x within the domain, arccos x returns the unique θ in [0, π] such that cos θ = x. In particular, arccos(0.5) equals π/3, which is 1.0471975512 radians or 60 degrees.

Key properties include the identity cos(arccos x) = x for all x in [-1, 1], and arccos x ∈ [0, π]. The arccos function is the inverse of the cosine function restricted to the domain [0, π]. Related transcedental relations include arccos x + arcsin x = π/2 for x in [-1, 1]. The derivative of arccos is d/dx arccos x = -1/√(1 - x^2) for x in (-1, 1), indicating arccos is decreasing on its domain.

In practical use, arccos is available as a standard function in programming languages and calculators under names such as acos or arccos, typically returning results in radians. Applications span trigonometry, geometry, and various engineering and physics computations where angle determination from a cosine value is required.