# Documentation/Calc Functions/ASIN

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## Function name:

ASIN

## Category:

Mathematical

## Summary:

Calculates the inverse trigonometric sine (arcsine or arcsin) of a real number. The value returned is the principal value and lies in the range [-π/2, π/2] radians.

## Syntax:

ASIN(**Number**)

## Returns:

Returns a real number in the range [-π/2, π/2] that is the inverse trigonometric sine of **Number** in radians.

## Arguments:

**Number** is a real number in the range [-1, 1], or a reference to a cell containing that number, whose inverse trigonometric sine is to be calculated.

- If
**Number**is non-numeric, then ASIN reports a #VALUE! error.

- If
**Number**lies outside the range [-1, 1], then ASIN reports a #NUM! error.

## Additional details:

- To return the angle in degrees, use the DEGREES function.
- Alternatively multiply by 180/PI() to convert the result from radians to degrees.

The formula for the inverse trigonometric sine of x is:

[math]\displaystyle{ \arcsin(x) ~=~ \sum_{n=0}^{\infty } \left ( \frac{(2n)!}{2^{2n}(n!)^2(2n+1)} \right )x^{2n+1} }[/math]

The figure below illustrates the function ASIN.

## Examples:

Formula | Description | Returns |
---|---|---|

=ASIN(-1) | Inverse trigonometric sine of -1. | -1.5707963267949 (-π/2) |

=ASIN(D1) where cell D1 contains the number 0.5. | Inverse trigonometric sine of 0.5. | 0.523598775598299 (π/6) |

=DEGREES(ASIN(0.5)) | Inverse trigonometric sine of 0.5, converted to degrees. | 30 |

=ASIN(-0.5)*180/PI() | Inverse trigonometric sine of -0.5, converted to degrees. | -30 |

=DEGREES(ASIN(SIN(RADIANS(60))) | An angle of 60° is converted to radians, its sine is taken, then the inverse sine of that value is calculated, and finally the result is converted back to degrees. | 60 |

## Related LibreOffice functions:

## ODF standard:

## Equivalent Excel functions:

ASIN