COT 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.

COT calculates cotangent, mathematically cos(x)/sin(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.

=COT(Number)

Supply one numeric argument. The argument is an angle in radians; degrees require an explicit RADIANS conversion. 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.

COT accepts an angle in radians. In a right-triangle interpretation, it is adjacent length divided by opposite length. At 0.5 radians the result is about 1.830487721712. For a degree-valued angle in A2, use =COT(RADIANS(A2)); do not feed a degree count directly to a radian function.

The identity COT(x)=COS(x)/SIN(x) applies away from a zero denominator. COT(−x)=−COT(x), which explains the paired signs in the table. A reciprocal check COT(x)×TAN(x)=1 works only where both factors are defined. Cotangent is not the inverse function that returns an angle from a ratio.

Cotangent has poles at integer multiples of π, including zero. A computed PI() is a nearby floating-point value, not exact π, so the very large finite result in the diagnostic table is consistent with evaluation near a pole. It is not a finite mathematical value at the pole.

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.

sin, cos, tan.

• 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.