# asin() Function & Examples

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

## asin

#### asin(x)

Try it yourself:

```calculio
asin(0.5)
asin(sin(0.5))
```

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

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

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

---

## asin(): Finding an Angle from Its Sine

**asin()** returns the principal angle whose sine equals the input. It reverses [sin()](https://calcul.io/function/sin/index.md) for its principal interval and is widely used to recover an angle from a vertical ratio, normalized coordinate, or measured signal.

## Real values and range

For real results, asin(x) requires −1 ≤ x ≤ 1 and returns an angle from −π/2 to π/2. Thus asin(0) is 0 and asin(1) is π/2. An input outside the interval cannot be a real sine; check normalization and rounding before assuming the calculation is wrong.

For example, after dividing an opposite side by a hypotenuse, asin gives the acute signed angle associated with that ratio. Clamp a value that should theoretically be in range using [min()](https://calcul.io/function/min/index.md) and [max()](https://calcul.io/function/max/index.md) when floating-point noise is the only source of overflow.

## Choosing the correct inverse

Sine has the same value at more than one angle, so asin cannot recover a unique full-circle direction. When both coordinates are available, use [atan2()](https://calcul.io/function/atan2/index.md). For cosine-derived ratios use [acos()](https://calcul.io/function/acos/index.md); for tangent ratios use [atan()](https://calcul.io/function/atan/index.md).

Keep results in radians when passing them back to sin or combining them with other mathematical functions. Convert to degrees only for a human-facing display, and verify by evaluating sin(asin(x)).

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