acot(): Recovering an Angle from a Cotangent

acot() returns a principal angle whose cotangent equals the input. Cotangent is the reciprocal of tan(), so acot is useful when a ratio is naturally expressed as adjacent divided by opposite. It appears in analytic geometry and in transformations that use cotangent directly.

Principal values and ambiguity

Trigonometric inverses return one representative angle, not every possible solution. The exact principal interval for acot is convention-dependent across software, so check the displayed result and use the same convention throughout a model. A cotangent value alone cannot distinguish all quadrants because cotangent repeats every π radians.

For a coordinate pair, atan2() is usually a better tool than dividing values and taking an inverse: it retains signs and handles axis cases explicitly. If you do use a reciprocal relationship, remember that 1/x is undefined at zero; protect that case with equal() or conditional logic.

Checking a calculation

Verify a result by applying cot() to it. Keep angle units in radians for consistency with the other trigonometric functions. acot is related to atan(), but replacing one with π/2 minus the other must be done with care around zero and branch boundaries.

In practice, state the intended output interval in documentation. That makes an inverse-cotangent calculation reproducible even when it is moved to another mathematical library.