Documentation/Calc Functions/TAN
TDF LibreOffice Document Liberation Project Community Blogs Weblate Nextcloud Redmine Ask LibreOffice Donate
Function name:
TAN
Category:
Mathematical
Summary:
Calculates the trigonometric tangent (tan) of an angle expressed in radians.
Syntax:
TAN(Number)
Returns:
Returns a real number that is the trigonometric tangent 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 trignometric tangent is to be calculated.
- If Number is non-numeric, then TAN 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 tangent of x is:
[math]\displaystyle{ \tan(x)~=~\frac{1}{\cot(x)}~=~\frac{\sin(x)}{\cos(x)} }[/math]
Mathematically, the tangent 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, TAN does not report errors for arguments close to these values. You should be aware that TAN will return large positive or negative results for odd multiples of π/2.
The figure below illustrates the function TAN.
Examples:
| Formula | Description | Returns |
|---|---|---|
| =TAN(1) | Trigonometric tangent of 1 radian. | 1.5574077246549 |
| =TAN(D1) where cell D1 contains the number -0.5. | Trigonometric tangent of -½ radian. | 0.54630248984379 |
| =TAN(PI()/4) | Trigonometic tangent of π/4 radians. | 1 |
| =TAN(RADIANS(45)) | Trignometric tangent of 45°, after first converting the angle from degrees to radians. | 1 |
| =DEGREES(ATAN(TAN(RADIANS(60))) | An angle of 60° is converted to radians, its tangent is taken, then the inverse tangent 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:
TAN