ACOTH in Collabora Office: Invert Hyperbolic Cotangent Outside the Unit Interval

• Introduced: original Collabora release and launch date are not established by the sources reviewed.
• Availability: documented in Collabora Office 26.04 help, scoped to the desktop-help release.
• Platform scope: support in every online or mobile deployment is not inferred from desktop documentation.
• Checked: October 14, 2026. Direct function-specific documentation and independent numerical examples; no native Collabora test was performed.

=ACOTH(number)

The permitted real inputs satisfy ABS(number)>1. This differs from ATANH, whose real inputs lie strictly inside the unit interval. The two domains should not be interchanged.

ACOTH is a hyperbolic inverse, not an angle-returning circular arccotangent. ACOT serves the circular case. Do not insert a degrees-to-radians conversion into a dimensionless ACOTH calculation.

The examples use English function names. Their decimal outputs are rounded mathematical expectations based on the documented function, without native Collabora execution.

Enter −3, −2, 2, 3 in A2:A5. In B2 enter and fill down:

=ACOTH(A2)

Expected B2:B5, approximately: −0.346573590, −0.549306144, 0.549306144, 0.346573590. Opposite inputs produce opposite outputs. Increasing a positive input from 2 to 3 makes the positive inverse result smaller.

That decrease is consistent with the hyperbolic cotangent relationship. Do not assume every inverse function grows as its input grows without examining the selected function and branch.

Inputs −1, −0.5, 0, 0.5, 1 all lie outside the documented real domain for ACOTH. The reference says these cases produce an error; this guide does not assign an exact displayed error label to every client.

Inputs −1.5 and 1.5 are valid and give approximately −0.804718956 and 0.804718956. The strict greater-than-one magnitude requirement is why 1 itself differs from 1.5.

Validate a source ratio before using it in a longer expression. A numeric cell merely formatted to display 1 can store a value on either side of the boundary.

=ACOTH(1.1)
=ACOTH(1.5)
=ACOTH(2)

Expected results: approximately 1.522261219, 0.804718956, 0.549306144. As a valid positive input approaches 1 from above, the inverse grows.

This does not justify rounding a borderline input to an allowed value. Any adjustment changes the data and should follow an explicit model or measurement policy. Keep the unrounded source available for diagnosis.

For permitted real inputs:

=ACOTH(A2)
=ATANH(1/A2)

At A2=2, both are approximately 0.549306144. At A2=−2, both are approximately −0.549306144. Taking the reciprocal moves a magnitude greater than 1 into ATANH’s open domain.

This identity helps distinguish inverse from reciprocal. ACOTH(2) is not 1/2. Instead, the reciprocal 0.5 is passed through a different inverse function, ATANH, to obtain the same hyperbolic argument.

The identity is a mathematical control, not a guarantee that every equivalent expression has identical floating-point behavior near a boundary or at extreme magnitudes.

For valid inputs, another identity is:

=0.5*LN((A2+1)/(A2-1))

At A2=3, the fraction is 2 and half its natural logarithm is approximately 0.346573590. At A2=−3, the fraction is 0.5 and the result is approximately −0.346573590.

The logarithm’s argument remains positive on both permitted branches. For inputs within the excluded interval, the expression either has an invalid real logarithm or a problematic denominator; it does not extend the documented real function to that interval.

Use the dedicated function for the intended operation. Direct arithmetic near a boundary can magnify cancellation or rounding, and this article has not benchmarked the competing formulations.

ACOTH is paired with hyperbolic cotangent, conventionally written as COSH(x)/SINH(x) where defined. For an input of 2, applying that ratio to ACOTH(2) reconstructs approximately 2:

=COSH(ACOTH(2))/SINH(ACOTH(2))

The functions COSH and SINH make this identity explicit without confusing it with circular cosine or sine.

Preserve the input scale and meaning. A mathematically valid number outside the unit interval is not evidence that a particular real-world model should use ACOTH.

Check the input’s magnitude, the strict boundary and whether you intended ATANH or ACOT instead. Test one positive and one negative allowed value as well as a deliberately rejected endpoint.

All ordinary examples here use finite real numbers. Complex-valued continuations, arbitrary text coercion and client-specific error displays remain outside the guide’s verified scope.

• Collabora Office 26.04: ACOTH.
• Editorial testing standards.

The official section supplies the product-specific definition and documented domain or angle branch. Original worked values were independently calculated. Native execution, extreme-value benchmarks and broader client compatibility remain unverified.