ACOS Function (OpenOffice Calc)
The ACOS function in OpenOffice Calc returns the arccosine (inverse cosine) of a value, in radians. Learn syntax, domain limits, examples, and best practices.
The ACOS function in OpenOffice Calc returns the arccosine (inverse cosine) of a value. The result is an angle in radians whose cosine equals the input. ACOS is essential for geometry, physics, engineering, vector math, and any calculation where you need to recover an angle from a ratio.
This guide provides syntax, domain rules, examples, advanced techniques, common errors, and best practices, making it one of the most complete ACOS references available for OpenOffice Calc.
What the ACOS Function Does
- Returns the angle whose cosine equals the input
- Output is in radians
- Input must be between −1 and 1
- Useful for triangle geometry, dot products, and inverse trig calculations
- Works across sheets
ACOS is ideal when you need to recover an angle from adjacent/hypotenuse ratios or vector dot products.
Syntax
ACOS(number)
Arguments:
- number — A value between −1 and 1
Convert to degrees using:
ACOS(x) * 180 / PI()
Domain Rules
| Input | Valid? | Notes |
|---|---|---|
| −1 ≤ x ≤ 1 | ✔ | Required |
| x < −1 or x > 1 | ✘ | Undefined |
| text | ✘ | Error |
Mathematically:
[ \text{acos}(x) \text{ is defined only for } -1 \le x \le 1 ]
Basic Examples
Arccosine of 0.5
=ACOS(0.5)
Result (radians): 1.047197551
Convert arcsine to degrees
=ACOS(0.5) * 180 / PI()
Result: 60
ACOS using a cell reference
=ACOS(A1)
Convert degrees to radians before applying COS, then invert
=ACOS(COS(RADIANS(60)))
Advanced Examples
Recover angle from adjacent/hypotenuse ratio
=ACOS(Adjacent / Hypotenuse)
Angle between two vectors (dot product)
Given vectors (x1,y1,z1) and (x2,y2,z2):
=ACOS( (x1*x2 + y1*y2 + z1*z2) / (SQRT(x1^2+y1^2+z1^2) * SQRT(x2^2+y2^2+z2^2)) )
ACOS across sheets
=ACOS(Sheet1.A1)
ACOS in array formulas
=ACOS(A1:A10)
Confirm with Ctrl+Shift+Enter.
Recover angle from normalized vector
=ACOS(X / Length)
Solve for angle in a right triangle
=ACOS(Adj / Hyp)
Compute longitude from spherical coordinates
=ACOS(X / Radius)
Convert arcsine result to degrees
=DEGREES(ACOS(A1))
Common Errors and Fixes
ACOS returns Err:502 (Invalid argument)
Occurs when:
- Input < −1 or > 1
- Input is text
- Input is empty
- A malformed reference is used
ACOS returns unexpected results
Possible causes:
- Forgetting that output is in radians
- Using degrees without converting
- Ratios slightly outside range due to rounding
ACOS ignores values you expected it to include
ACOS ignores:
- Text numbers (
"123") - Empty cells
- Logical values
- Errors
ACOS includes values you expected it to ignore
ACOS includes:
- Dates
- Times
- Numeric results of formulas
Err:508 — Missing parenthesis
Usually caused by:
- Missing
) - Using commas instead of semicolons
Best Practices
- Always check that input is between −1 and 1
- Convert radians to degrees when needed
- Use ACOS for dot‑product angle calculations
- Use named ranges for triangle sides and vector components
- Pair ACOS with COS for reversible transformations