COSH Function in ONLYOFFICE Spreadsheet Editor: Hyperbolic Cosine, Symmetry, and Practical Examples

COSH produces the same mathematical output for positive and negative inputs of equal magnitude. It appears in hanging-chain (catenary) models, some smooth penalty functions, and exponential identities. It is not the ordinary circular COS function.

Mathematically, cosh(x) = (e^x + e^(-x)) / 2. This identity explains the intended numerical values; it does not independently prove how a particular ONLYOFFICE release evaluates unusual inputs.

=COSH(number)

The argument order is unambiguous because COSH has just one input. Enter the leading = when typing a spreadsheet formula. The English function name and syntax above are verified against ONLYOFFICE’s COSH reference, accessed 2026-10-13. The official index places it in Math and Trigonometry Functions. This is a hyperbolic function; an input of 1 is a numeric argument, not a one-degree measurement.

1. Open a blank sheet. Enter Input x in A1, COSH result in B1, and Purpose in C1.
2. Enter the following values in cells A2:A9, as numbers, not as text. Use English-formula language and a decimal-point regional setting for the notation shown.
3. In B2 type =COSH(A2) and press Enter. Copy B2 down through B9 so that each result refers to its own A-row.
4. Compare your editor’s output with the mathematical expectations below; numerical display precision may differ. This workflow is proposed for human verification and was not executed natively during research.

The displayed decimal places are a presentation choice, not a claim that the editor stores exactly those decimal strings. To see the consequence of copying a relative reference, change A4 from 1 to 2 and compare B4 with the existing B6 result before restoring A4.

• =COSH(0) → 1 (The anchor at zero. Expected, not native-observed.)
• =COSH(1) → 1.543080634815 (The positive unit input. Expected, not native-observed.)
• =COSH(-1) → 1.543080634815 (A negative input; check symmetry. Expected, not native-observed.)
• =ROUND(COSH(2),4) → 3.7622 (Round the numeric result to four decimal places (ROUND is separately documented by ONLYOFFICE). Expected, not native-observed.)

Symmetric penalty

If the deviation is entered in A4 (1), =COSH(A4)-1 gives about 0.5430806348. Changing A4 to -1 gives the same mathematical penalty.

Hanging-chain curve

With a scale parameter of 2, a simplified catenary value =2*COSH(A4/2) for A4 = 1 should be approximately 2.2552519304. This demonstrates a shape, not an engineering design calculation.

Identity audit

=COSH(A4)^2-SINH(A4)^2 is mathematically 1. If the spreadsheet displays a value slightly different from 1, inspect floating-point precision before treating it as a logical error.

• cosh(0) = 1.
• cosh(-x) = cosh(x), so it is an even function.
• For real x, cosh(x) ≥ 1, with its minimum at x = 0.

These are properties of real-number hyperbolic functions, verified through independent calculation, not a claim about text coercion, overflow exceptions, or a specific editor release. They can be used as consistency checks but should not replace native product testing.

A bare =COSH() is missing the required number argument. The vendor page does not explicitly state what exact error code or message ONLYOFFICE will display in every edition; do not assume an Excel error code without reproducing it in ONLYOFFICE. The same caution applies to text inputs, invalid cells and very large magnitudes.

• English notation used here: =COSH(number) with a decimal point in examples. The ONLYOFFICE Insert Functions guide documents a leading equal sign, parenthesized arguments, and formula insertion through the Formula tab or Shift+F3. Its examples use comma argument separators (this function has only one argument).
• Formula language and regional settings: ONLYOFFICE Advanced Settings documents configurable formula language and regional number separators. Choose English if you want the displayed function names in this guide; the exact localized function name and keyboard entry were not tested.
• Web versus desktop: The vendor publishes a unified, unversioned Spreadsheet Editor function reference. Its settings documentation distinguishes some online and desktop features, but does not establish COSH’s first supported release or identical historical behaviour. The official Docs 10.0 announcement (October 2026) is not treated as evidence that COSH was newly introduced then.
• Other spreadsheet applications: The formulas are conceptually familiar across many spreadsheets, but no native Excel, Google Sheets, LibreOffice, or cross-file interchange test was performed. Syntax/precision differences must be checked before relying on interoperability.
• Validation: Source existence, argument count, argument meaning, and insertion instructions = vendor documentation review. Numeric results, identities, and bounds = independent Python mathematical calculation. Native execution in any ONLYOFFICE release, screenshots, exact errors, calculation-engine precision and locale permutations = not performed.

For a signed hyperbolic curve see SINH; for a bounded ratio between -1 and 1 see TANH.

• SINH reference (official ONLYOFFICE).
• COSH reference (official ONLYOFFICE).
• TANH reference (official ONLYOFFICE).
• ROUND reference (official ONLYOFFICE; used in rounding example).
• EXP reference (official ONLYOFFICE; used to explain the mathematical identities).

1. ONLYOFFICE Help Center, COSH function — function category, purpose, official one-argument syntax and type. English unversioned page; no first-supported editor release supplied.
2. ONLYOFFICE Help Center, Spreadsheet Editor — Inserting functions — formula-entry workflow, = convention, arguments, and availability of the function-insertion UI.
3. ONLYOFFICE Help Center, Spreadsheet Editor — Advanced Settings — configurable formula language/regional number separators and online-versus-desktop distinctions.
4. ONLYOFFICE Help Center, ROUND function and EXP function — auxiliary documented functions used in worked identities/rounding. These sources do not validate this page’s calculations in an actual workbook.