# acot() Function & Examples

Use the acot() trigonometry function in Calcul.io. Review its syntax, edit working examples, understand the result, and explore related math functions.

## acot

#### acot(x)

Try it yourself:

```calculio
acot(0.5)
acot(cot(0.5))
acot(2)
```

[cot](https://calcul.io/function/cot/index.md)

[atan](https://calcul.io/function/atan/index.md)

---

## acot(): Recovering an Angle from a Cotangent

**acot()** returns a principal angle whose cotangent equals the input. Cotangent is the reciprocal of [tan()](https://calcul.io/function/tan/index.md), 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()](https://calcul.io/function/atan2/index.md) 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()](https://calcul.io/function/equal/index.md) or conditional logic.

## Checking a calculation

Verify a result by applying [cot()](https://calcul.io/function/cot/index.md) to it. Keep angle units in radians for consistency with the other trigonometric functions. acot is related to [atan()](https://calcul.io/function/atan/index.md), 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.

[All functions](https://calcul.io/functions/index.md)