# Documentation/Calc Functions/COS

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## Function name:

COS

## Category:

Mathematical

## Summary:

Calculates the trigonometric cosine (cos) of an angle expressed in radians.

## Syntax:

COS(**Number**)

## Returns:

Returns a real number in the range [-1, 1] that is the trigonometric cosine of the specified angle.

## Arguments:

**Number** is a real number, or a reference to a cell containing that number, that is the angle in radians whose trigonometric cosine is to be calculated.

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

## Additional details:

If your angle is expressed in degrees, either multiply by PI()/180 or use the RADIANS function to convert to radians.

The formula for the trigonometric cosine of x is:

[math]\displaystyle{ \cos(x)~=~\sum_{n=0}^{\infty }\frac{(-1)^{n}}{(2n)!}~x^{2n} }[/math]

The figure below illustrates the function COS.

## Examples:

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

=COS(1) | Trigonometric cosine of 1 radian. | 0.54030230586814 |

=COS(D1) where cell D1 contains the number -0.5. | Trigonometric cosine of -½ radian. | 0.877582561890373 |

=COS(PI()*2) | Trigonometric cosine of 2π radians. | 1 |

=COS(RADIANS(60)) | Trigonometric cosine of 60°, after first converting the angle from degrees to radians. | 0.5 |

=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:

## Equivalent Excel functions:

COS