COTH Function (OpenOffice Calc)

• Introduced: First release not established; documented by OpenOffice.org 3.3.
• Supported in: Apache OpenOffice 4.1.16; this identifies a verified release, not a final supported version.
• Scope: Desktop Calc, English function names and semicolon-separated formulas.
• Checked: October 14, 2026. Eight reference formulas and the listed diagnostics were recalculated from generated native ODF in 4.1.16 on Linux x86-64, Build 9816. Source and independent reference calculations were also checked.

COTH calculates hyperbolic cotangent, mathematically cosh(x)/sinh(x). It returns a real numeric value for a valid finite input where the defining denominator is nonzero. The implementation evaluates the reciprocal directly, so denominator zeros and floating-point behavior matter. Release entry.

=COTH(Number)

Supply one numeric argument. The argument is a real, dimensionless input; this hyperbolic function has no intrinsic degree unit. The observed TRUE argument becomes 1, and a referenced empty cell becomes 0. Non-numeric text and an extra argument produce errors in the tested cases.

The native column records the saved 4.1.16 results. The independent values use high-precision mathematics; displayed decimals are rounded to twelve places. Integer results remain exact in these small cases.

Use COTH for a hyperbolic ratio, not an ordinary angle. For a dimensionless input 0.5, COTH returns about 2.163953413739. If a model uses x=t/τ, enter that dimensionless ratio in A2 and use =COTH(A2). Converting this argument from degrees would change the model without justification.

COTH(x)×TANH(x)=1 for nonzero real x. It is odd, so COTH(−x)=−COTH(x), and its magnitude exceeds 1 for every finite nonzero real input. As positive x grows it approaches 1; as negative x decreases it approaches −1. The positive table values decrease toward 1 without becoming a probability.

Zero is the real pole. For sufficiently small nonzero x, the leading behavior is approximately 1/x; this explains why values increase sharply near zero. The finite tables do not test extreme magnitudes, overflow or a near-zero accuracy guarantee.

These additional formulas were recalculated from the same generated ODF input. H5 is a deliberately empty cell where referenced. Error displays are retained as errors, even when an ODS numeric attribute stores zero.

SINH, COSH, TANH.

• Function-specific release entry

The generated ODF input produced the informational load warning “Not all attributes could be read.” After it was acknowledged, the sheet was hard-recalculated and saved separately. Every formula identity, input label and tested result was reconciled, including repeated spaces represented with ODF text elements. This does not certify every style attribute. The separately prepared XLSX input was not executed. A deliberately stale SUM cache changed from 999999 to 3, and an uncached SUM returned 7 after hard recalculation. Native evidence covers the eight reference formulas and listed diagnostics only. Other explanatory compositions are independent mathematical checks; other releases, locales and extreme-value behavior were not established by this run.