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ACOTH Function (LibreOffice Calc)

Mathematical Intermediate LibreOffice Calc LibreOffice 4.0

The ACOTH function returns the inverse hyperbolic cotangent of a number. The result is expressed in radians and is used in advanced mathematics, engineering, and scientific modeling.

The **ACOTH** function returns the **inverse hyperbolic cotangent** of a number. The result is an angle in **radians**, and the function is commonly used in engineering, physics, and advanced mathematical modeling involving hyperbolic functions.

What the ACOTH Function Does

  • Computes the inverse hyperbolic cotangent
  • Returns an angle in radians
  • Accepts values greater than 1 or less than –1
  • Useful in scientific, engineering, and computational mathematics

Syntax

ACOTH(number)

Arguments

  • number:
    A numeric value > 1 or < –1.

Basic Examples

Inverse hyperbolic cotangent of a value

=ACOTH(2)
→ 0.549306144

=ACOTH(-3)
→ -0.34657359

Convert result to degrees

=DEGREES(ACOTH(2))

Using a cell reference

=ACOTH(A1)

Advanced Examples

Compute ACOTH using its logarithmic identity

=0.5 * LN((A1 + 1) / (A1 - 1))

Normalize input to avoid domain errors

=ACOTH(IF(ABS(A1) <= 1; NA(); A1))

Hyperbolic modeling example

=ACOTH(COTH(A1))

Engineering formula example

=ACOTH((V + I) / (V - I))

Edge Cases and Behavior Details

ACOTH returns a numeric value (radians)

Accepts:

  • Numbers > 1
  • Numbers < –1
  • Expressions that evaluate to numbers

Invalid input → Err:502

Behavior details

  • Domain is (–∞, –1) ∪ (1, ∞)
  • Output is in radians
  • ACOTH is undefined for values between –1 and 1
  • Use DEGREES() to convert the result

ACOTH of an error → error propagates

Common Errors and Fixes

Err:502 — Invalid argument

Cause:

  • Input between –1 and 1
  • Input is text

Fix:

  • Validate domain
  • Convert text to number with VALUE

Unexpected result

Cause:

  • Forgetting ACOTH returns radians
  • Using values close to ±1 (results approach ±∞)

Fix:

  • Wrap with DEGREES
  • Validate numeric stability

Best Practices

  • Always validate that |number| > 1
  • Convert to degrees when presenting angles
  • Use ACOTH with ASINH, ACOSH, and ATANH for full hyperbolic workflows
  • Combine with LN and EXP for scientific modeling
ACOTH is your inverse‑hyperbolic‑cotangent tool — essential for engineering, physics, and advanced mathematical modeling.
  • Use ACOT for inverse cotangent
  • Use ATANH for inverse hyperbolic tangent
  • Use COTH (if available) for forward hyperbolic cotangent
  • Use DEGREES and RADIANS for angle conversion

By mastering ACOTH and its companion functions, you can build precise, reliable hyperbolic and scientific models in LibreOffice Calc.