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ACOT Function (LibreOffice Calc)

Mathematical Intermediate LibreOffice Calc LibreOffice 4.0

The ACOT function returns the inverse cotangent (arccotangent) of a number. The result is expressed in radians and is used in trigonometry, geometry, and engineering calculations.

Verification status: Consult the documentation and examples below. Native application testing has not been documented for this guide. How formula examples are checked

The **ACOT** function returns the **inverse cotangent** (arccotangent) of a number. The result is an angle in **radians**, commonly used in trigonometry, geometry, and engineering applications where cotangent relationships arise.

What the ACOT Function Does

  • Computes the inverse cotangent of a value
  • Returns an angle in radians
  • Accepts any real number
  • Useful in geometry, signal processing, and advanced trigonometric modeling

Syntax

ACOT(number)

Arguments

  • number:
    A numeric value representing the cotangent of an angle.

Basic Examples

Inverse cotangent of a value

=ACOT(1)
→ 0.785398163 (π/4 radians)

=ACOT(0.5)
→ 1.107148718

Convert result to degrees

=DEGREES(ACOT(1))
→ 45

Using a cell reference

=ACOT(A1)

Advanced Examples

Compute ACOT using ATAN identity

=ATAN(1 / A1)

Avoid division-by-zero errors

=ACOT(IF(A1=0; 1E-12; A1))

Angle between two vectors using cotangent form

=ACOT( (A1*B1 + A2*B2) / (A1*B2 - A2*B1) )

Engineering formula example

=ACOT((R / X))

Combine with DEGREES for readable output

=DEGREES(ACOT(A1))

Edge Cases and Behavior Details

ACOT returns a numeric value (radians)

Accepts:

  • Any real number
  • Expressions that evaluate to numbers

Invalid input → Err:502

Behavior details

  • Domain is (–∞, ∞)
  • Output is in radians
  • ACOT(0) returns Ï€/2
  • ACOT preserves sign symmetry: ACOT(–x) = Ï€ – ACOT(x)

ACOT of an error → error propagates

Common Errors and Fixes

Err:502 — Invalid argument

Cause:

  • Input is text
  • Input cannot be coerced to a number

Fix:

  • Convert text to number with VALUE
  • Validate numeric input

Unexpected angle

Cause:

  • Forgetting ACOT returns radians
  • Using ATAN(1/x) without handling x=0

Fix:

  • Wrap with DEGREES
  • Use safe division patterns

Best Practices

  • Convert to degrees when presenting angles to users
  • Use ACOT with ATAN, ACOS, and ASIN for complete inverse‑trig workflows
  • Normalize inputs to avoid division‑by‑zero errors
  • Use ACOTH for hyperbolic inverse cotangent
ACOT is your inverse‑cotangent workhorse — essential for geometry, engineering, and any model involving cotangent‑based angle relationships.
  • Use ATAN for inverse tangent
  • Use ACOTH for inverse hyperbolic cotangent
  • Use DEGREES and RADIANS for angle conversion
  • Use PI() for circle and rotation calculations

By mastering ACOT and its companion functions, you can build precise, reliable trigonometric and geometric models in LibreOffice Calc.