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