Acos (arccosine)

Syntax

Acos(<number>)

π Acos(ratio) → angle_rad (Triangles)

Description

Acos returns the arccosine: the angle, in radians, whose cosine is the input. It is the inverse of Cos. Acos(-1) is π.

Technical Description

Acos(x: NUMBER) → NUMBER. Returns acos(x) in radians, in [0, π] (Math.acos). The argument must lie in [−1, 1], else an evaluation error, as PostgreSQL raises. NULL input returns NULL. PURE, DETERMINISTIC. Floating-point result. SQL's ACOS(x).

Examples

Angle between two unit vectors from their dot product:

π a, b, Acos(dot) → angle_rad (Pairs)

PROJECT a, b, Acos(dot) -> angle_rad (Pairs)

Limitations

Errors on an argument outside [−1, 1]; a dot product computed in floating point can land a hair outside, so clamp it with LEAST/GREATEST first. Returns radians. NUMBER only; NULL in → NULL out.

Alternatives

Asin and Atan2 recover an angle from other ratios.

See Also

cos, asin, atan2, degrees