# Documentation/Calc Functions/ACOS

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## Function name:

ACOS

## Category:

Mathematical

## Summary:

Calculates the inverse trigonometric cosine (arccosine or arccos) of a real number. The value returned is the principal value and lies in the range [0,π] radians.

## Syntax:

ACOS(**Number**)

## Returns:

Returns a real number in the range [0,π] that is the inverse trigonometric cosine 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 cosine is to be calculated.

- If
**Number**is non-numeric, then ACOS reports a #VALUE! error. - If
**Number**lies outside the range [-1, 1], then ACOS 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 cosine of x is:

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

The figure below illustrates the function ACOS.

## Examples:

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

=ACOS(−1) | Inverse trigonometric cosine of -1. | 3.14159265358979 (π) |

=ACOS(D1) where cell D1 contains the number 0.5. | Inverse trigonometric cosine of 0.5. | 1.0471975511966 (π/3) |

=DEGREES(ACOS(0.5)) | Inverse trigonometric cosine of 0.5, converted to degrees. | 60 |

=ACOS(−0.5)*180/PI() | Inverse trigonometric cosine of -0.5, converted to degrees. | 120 |

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

## Related LibreOffice functions:

## ODF standard:

## Related (or similar) Excel functions:

ACOS