# Documentation/Calc Functions/SEC

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## Function name:

SEC

## Category:

Mathematical

## Summary:

Calculates the trigonometric secant (sec) of an angle expressed in radians.

## Syntax:

SEC(**Number**)

## Returns:

Returns a number that is the trigonometric secant of the specified angle. The value returned is a real number x, such that x ≤ -1 or x ≥ 1 (x cannot lie in the range (-1, 1)).

## Arguments:

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

- If
**Number**is non-numeric, then SEC 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 secant of x is:

[math]\displaystyle{ \sec(x)~=~\frac{1}{\cos(x)} }[/math]

Mathematically, the secant of any odd multiple of π/2, i.e. {......-3π/2, -π/2, π/2, 3π/2.....} is undefined. However, because of the inherent inaccuracy in representing π numerically, SEC does not report errors for arguments close to these values. You should be aware that SEC will return large positive or negative results for odd multiples of π/2.

The figure below illustrates the function SEC.

## Examples:

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

=SEC(1) | Trigonometric secant of 1 radian. | 1.85081571768093 |

=SEC(D1) where cell D1 contains the number -2. | Trigonometric secant of -2 radians. | −2.40299796172238 |

=SEC(PI()/4) | Trigonometric secant of π/4 radians. | 1.4142135623731 |

=SEC(RADIANS(60)) | Trigonometric secant of 60°, after first converting the angle from degrees to radians. | 2 |

## Related LibreOffice functions:

## ODF standard:

## Related (or similar) Excel functions:

SEC since v.2013.