ACOTH Function (LibreOffice Calc)

• 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

ACOTH(number)

Arguments

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

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)

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))

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

• 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

• 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.