COTH in Collabora Office: Work with Hyperbolic Cotangent Ratios

• 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. Function-specific documentation and independent numerical examples; no native Collabora test was performed.

=COTH(number)

number is the numeric hyperbolic argument. For nonzero real x, COTH(x) equals COSH(x)/SINH(x), or 1/TANH(x). COSH, SINH and TANH provide those related functions.

Do not automatically apply RADIANS. A hyperbolic model commonly uses a dimensionless argument formed from a ratio of quantities, rather than a degree angle. Follow the units and scaling defined by the model instead of inferring them from the word cotangent.

Enter −2, −1, −0.5, 0.5, 1, 2 in A2:A7. In B2 enter and fill down:

=COTH(A2)

COTH is odd: opposite nonzero inputs have opposite outputs of equal magnitude. For finite nonzero real inputs, its mathematical magnitude exceeds one. The positive branch approaches one as the input increases; it does not oscillate like circular cotangent.

In finite-precision arithmetic, a sufficiently large argument can yield a rounded value of one. The mathematical strict inequality is not a promise that every stored output remains distinguishable from one.

=COTH(1)
=COSH(1)/SINH(1)
=1/TANH(1)

Expected results: approximately 1.313035285 in all three cases. Use these as ordinary-input controls, not as a universal numerical-stability benchmark.

The ratio COSH(x)/SINH(x) can involve very large intermediate values for large x. Algebraic equivalence alone does not establish identical overflow behavior for every implementation. Use the dedicated function for the intended operation unless you have a tested reason to replace it.

Suppose a model defines its hyperbolic argument as a measurement divided by a positive characteristic scale. Put measurements 1, 2 and 4 in A2:A4 and the scale 2 in D1. Enter in B2 and fill down:

=COTH(A2/$D$1)

Expected results, approximately: 2.163953414, 1.313035285 and 1.037314721. The dollar signs keep the scale reference fixed when the formula is copied.

Both measurement and scale must use compatible units so their ratio is dimensionless. A scale of zero would invalidate the division before COTH could represent the intended model. A measurement of zero also reaches COTH’s mathematical singularity, even when the scale itself is valid.

This is an illustrative calculation pattern, not a claim that COTH is an appropriate model for every measured process. Preserve the model’s meaning and allowed input range in worksheet notes.

=ACOTH(COTH(1))
=COTH(1)^2-CSCH(1)^2

Expected results: approximately 1 and 1. ACOTH is the corresponding inverse function on its documented branches. CSCH supplies hyperbolic cosecant for the identity.

The inverse control uses an ordinary input where the computed COTH value remains safely above one. If a very large positive input produces a stored value rounded to exactly one, ACOTH’s strict domain would no longer permit that stored endpoint. Symbolic reversibility does not remove finite-precision boundaries.

COTH is mathematically undefined at zero because SINH(0) is zero. As a positive input approaches zero, COTH grows rather than tending to zero. For inputs 0.1, 0.5 and 1, expected values are approximately 10.033311132, 2.163953414 and 1.313035285.

Test a positive and a negative ordinary control, and reject inputs outside the model’s intended range before interpreting the output. The official section reviewed does not specify an exact displayed zero-input error code for every Collabora client, so this guide does not invent one.

No native zero, overflow or large-argument benchmark was performed. Retain the underlying input precision when comparing nearby cases.

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

The official section supplies the product-specific definition and angle-unit guidance where applicable. Worked models, identities and rounded outputs are independently calculated expectations. Native execution and broader client compatibility remain unverified.