# Documentation/Calc Functions/SIN

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## Function name:

SIN

## Category:

Mathematical

## Summary:

Calculates the trigonometric sine (sin) of an angle expressed in radians.

## Syntax:

SIN(**Number**)

## Returns:

Returns a real number in the range [-1, 1] that is the trigonometric sine 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 sine is to be calculated.

- If
**Number**is non-numeric, then SIN 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 sine of x is:

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

The figure below illustrates the function SIN.

## Examples:

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

=SIN(1) | Trigonometric sine of 1 radian. | 0.841470984807896 |

=SIN(D1) where cell D1 contains the number -0.5. | Trigonometric sine of -½ radian. | −0.479425538604203 |

=SIN(PI()/2) | Trigonometric sine of π/2 radians. | 1 |

=SIN(RADIANS(30)) | Trigonometric sine of 30°, after first converting the angle from degrees to radians. | 0.5 |

=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:

## Related (or similar) Excel functions:

SIN