COTH Function in ONLYOFFICE Spreadsheet Editor: Syntax, Examples and Compatibility

The named function and the syntax below are in the current, unversioned English ONLYOFFICE Docs Spreadsheet Editor documentation reviewed on 13 October 2026 (UTC). This is documentary support for the current reference, not a successful execution test in ONLYOFFICE Docs/web or Desktop Editors, and it is not a claim of support in all earlier versions, hosting editions, mobile apps, or imported Excel workbooks. The Docs changelog lists version 10.0.0 dated 10 October 2026; that changelog does not identify these particular functions as newly introduced in 10.0. Desktop release history is maintained separately, and no first-supported Desktop/web version has been established for this function.

Verification labels used in this guide: vendor documented = stated in a linked ONLYOFFICE source; independently calculated expectation = calculated outside ONLYOFFICE using mathematics/Python; native result = none obtained. Illustrations/screenshots were not fabricated or substituted for actual tests.

=COTH(number)

• number (required, numeric): One required numeric argument representing a hyperbolic angle in radians. Official ONLYOFFICE documentation additionally states |number| < 2²⁷. There is no optional argument or default.
• Argument order: one positional numeric argument only. Optional arguments/defaults: none.
• Return type: numeric real value for an in-domain mathematical input; the exact cell display can vary with number format.
• Mathematical domain: Real numbers other than zero, subject to the vendor-documented absolute-value limit. The documented limit is an input requirement; it does not itself guarantee successful calculation at very large magnitudes.
• Principal range / behaviour: For nonzero real inputs, the mathematical value has magnitude greater than 1, tending toward +1 for large positive arguments and toward −1 for large negative arguments.
• Units: The vendor labels the parameter as a hyperbolic angle in radians. Treat your worksheet input as a dimensionless hyperbolic argument. Applying a degrees-to-radians conversion to a general scaling parameter is not automatically appropriate.

Mathematical interpretation: coth(x) = cosh(x)/sinh(x) = 1/tanh(x) for x≠0. It is an odd function: coth(−x)=−coth(x). This mathematical identity is independently calculated, not vendor execution evidence.

1. Create an empty spreadsheet in the ONLYOFFICE Spreadsheet Editor, using its English formula language for the formulas shown.
2. Enter the numbers exactly as shown in the Input in A column below, beginning in A2 and going down one row per example; do not include the units, symbols, or quotation marks as part of the values.
3. In B2, enter =COTH(A2), press Enter, and fill the formula down the column. Numeric cells can be formatted to show ten decimal places.
4. Compare your result to the independently calculated expectation, allowing for display rounding and floating-point arithmetic. This guide does not claim that steps 1–3 were executed in either ONLYOFFICE product.

Interpreting the table: values are independent mathematical expectations rounded for readability, not screenshots or verified calculations performed in ONLYOFFICE. Values at very small magnitude may display in scientific notation when the worksheet format changes.

1. Cross-check against TANH

Set up: Enter D2 = 1, =COTH(D2) in E2, and =1/TANH(D2) in F2.

Expected output: Both ≈ 1.3130352855 (independently calculated, not native-tested).

Why it works: TANH provides a mathematically equivalent reciprocal, provided the input is nonzero.

2. Cross-check with COSH and SINH

Set up: Set D3 = -2, use =COTH(D3) in E3 and =COSH(D3)/SINH(D3) in F3.

Expected output: Both ≈ −1.0373147207 (independently calculated, not native-tested).

Why it works: The ratio explains the negative sign and the relationship among hyperbolic functions.

3. Guard the singularity at zero

Set up: Set D4 = 0 and enter =IF(D4=0,"undefined at zero",COTH(D4)) in E4.

Expected output: The intended text branch: undefined at zero (independently calculated, not native-tested).

Why it works: The formula avoids attempting a mathematically undefined value; precise native error strings are not asserted.

4. A clean rational identity with natural logarithm

Set up: Enter =COTH(LN(3)) in E5.

Expected output: 1.25 (independently calculated, not native-tested).

Why it works: Since cosh(ln 3)=5/3 and sinh(ln 3)=4/3, their ratio is 5/4. This independent result is a useful test fixture.

5. Measure the distance from the asymptote

Set up: Enter =COTH(2)-1 in E6.

Expected output: ≈ 0.0373147207 (independently calculated, not native-tested).

Why it works: For positive x, the difference from the horizontal asymptote +1 decreases as x grows.

Error-code caution: ONLYOFFICE documentation for this function does not establish exact error strings for every invalid input, coercion, overflow, or version. Thus this guide does not assert #NUM!, #DIV/0!, or other codes as observed in ONLYOFFICE. Record actual native outputs and version/edition before relying on undocumented error behavior.

The examples use English function names, decimal points and (where needed) comma-separated arguments. The official Insert Function guide explains that manual formulas begin with = and that arguments are separated by commas in its English instructions. The Advanced Settings page documents configurable formula language and regional decimal/thousands separators. Neither source establishes how this exact function was spelled or evaluated for every locale. Do not rewrite formulas using a different locale based only on habits from another spreadsheet program.

The vendor distinguishes the web/Docs editor from Desktop Editors and maintains separate release changelogs. The current function page does not state a first-supported version or guarantee parity across historical installations. Version-sensitive behaviour, real error results, large-value precision, workbook imports, mobile editions, and localized syntax therefore require native verification. A release-note mention of a related Spreadsheet Editor improvement must not be mistaken for a function introduction.

• TANH function — vendor function reference.
• COSH function — vendor function reference.
• SINH function — vendor function reference.
• ACOTH function — vendor function reference.
• IF function — vendor function reference.
• LN function — vendor function reference.
• Insert functions in ONLYOFFICE Spreadsheet Editor — function-selection, autocomplete and entry workflow.
• Spreadsheet Editor advanced settings — formula language, regions, and separators.

Does COTH use degrees?

The official argument is described as a hyperbolic angle in radians; mathematical hyperbolic functions ordinarily use dimensionless arguments.

What is COTH(0)?

It is undefined mathematically because hyperbolic sine is zero at zero. Exact application error behavior needs native validation.

Is COTH the same as 1/TANH?

They are mathematically equal for nonzero inputs, subject to finite-precision effects.

Verification limitations: Native Docs/web and Desktop execution, localized parsing, extreme-value precision, historical editions and runtime error behavior were not tested.