COT in ONLYOFFICE: Cotangent of a Radian Angle
How to use the ONLYOFFICE COT function: documented radians/numeric input, worksheet examples, reciprocal formulas, limitations and platform notes.
Verification status: Official documentation referenced; example outcomes independently reasoned or arithmetically checked where stated. Not executed in ONLYOFFICE Spreadsheet Editor. How formula examples are checked
Quick answer. COT(number) returns the cotangent of an angle given in radians. Mathematically, cotangent is cosine divided by sine wherever sine is nonzero. See ONLYOFFICE’s current COT reference for the vendor’s one-argument signature. The examples are independently calculated mathematical expectations; native ONLYOFFICE execution was not performed.
What COT does—and what its number means
Cotangent helps express the horizontal/vertical ratio of an incline and complements tangent in triangle geometry. The mathematical definition is:
COT(x)=COS(x)/SIN(x) whenever SIN(x)≠0. This identity is a mathematical derivation, not an execution claim for ONLYOFFICE.
Exact official syntax, arguments, and defaults
=COT(number)
| Argument | Position | Required? | Input type and unit described by ONLYOFFICE | Default |
|---|---|---|---|---|
number |
1 | Yes; the only documented argument | Numeric angle in radians; its absolute value must be strictly less than 2^27 (134,217,728) | No optional argument/default documented |
The official page explicitly states the strict bound abs(number)<2^27; an argument equal to the boundary is outside the documented input range. It does not establish a particular returned error code for violating that limit, nor specify how blank cells, quoted numerals or Boolean inputs are coerced. This guide uses ordinary numeric cells. Official evidence.
Documented radian angles: The values in column A are deliberately degrees for human readability, but the input actually given to SEC/CSC/COT is RADIANS(A2) and so on. This transformation is essential.
Reproduce the worksheet from a blank file
- Open an editable spreadsheet in ONLYOFFICE Spreadsheet Editor. Its current function-entry guide shows Formula → Function or manually entering a formula beginning with
=. - Put
angle (°)in A1 andCOT resultin B1. Type the following numeric values, one per row, into A2:A9: 30, 45, 60, 120, 135, 150, 210, 315. - Enter
=COT(RADIANS(A2))in B2 and fill down through B9. The row references should change automatically. Use English formula language for these exact names. - Compare B2:B9 to the independent mathematical expectations, not to claimed screenshots or observed runtime outputs:
| Cell / row | Value in column A | Enter in column B (or fill down) | Independently calculated expectation |
|---|---|---|---|
| A2 | 30 | =COT(RADIANS(A2)) |
≈ 1.7320508076 |
| A3 | 45 | =COT(RADIANS(A3)) |
≈ 1 |
| A4 | 60 | =COT(RADIANS(A4)) |
≈ 0.57735026919 |
| A5 | 120 | =COT(RADIANS(A5)) |
≈ -0.57735026919 |
| A6 | 135 | =COT(RADIANS(A6)) |
≈ -1 |
| A7 | 150 | =COT(RADIANS(A7)) |
≈ -1.7320508076 |
| A8 | 210 | =COT(RADIANS(A8)) |
≈ 1.7320508076 |
| A9 | 315 | =COT(RADIANS(A9)) |
≈ -1 |
- For extra verification, open Formula → Function and search for
COTas described in the vendor’s insertion instructions. This checks that the feature is exposed in your installation; it is not proof that every historical release supports it.
Additional reproducible formulas and independently calculated results
These are directly pasteable English-language examples in separate empty cells. They are expected results from independent mathematical calculations, not native ONLYOFFICE observations. Answers marked ≈ are rounded for display; compare a few decimals.
| English-locale formula | Mathematical expected result | Why it matters |
|---|---|---|
=COT(PI()/4) |
≈ 1 | cotangent of 45° |
=COT(PI()/6) |
≈ 1.7320508076 | cotangent of 30° |
=COT(PI()/3) |
≈ 0.57735026919 | cotangent of 60° |
=COT(-PI()/4) |
≈ -1 | cotangent is odd |
=3*COT(RADIANS(30)) |
≈ 5.1961524227 | horizontal run for 3-metre rise |
=COT(RADIANS(150)) |
≈ -1.7320508076 | quadrant II gives negative |
=COT(RADIANS(210)) |
≈ 1.7320508076 | quadrant III gives positive |
=COT(RADIANS(135)) |
≈ -1 | negative unit cotangent |
=COT(RADIANS(60))*TAN(RADIANS(60)) |
≈ 1 | identity near 1 |
=COS(RADIANS(30))/SIN(RADIANS(30)) |
≈ 1.7320508076 | independent ratio |
=1/TAN(RADIANS(45)) |
≈ 1 | reciprocal expression |
=ABS(COT(RADIANS(120))) |
≈ 0.57735026919 | positive magnitude of signed result |
Advanced applications and important mathematical limits
1. Estimate a horizontal run from an incline
For a right triangle with a vertical rise of 3 metres and an incline angle of 30° above the horizontal, cot(angle)=run/rise. Therefore =3*COT(RADIANS(30)) has an independently calculated horizontal run of about 5.19615242271 metres. This is a straight-line geometry example; do not confuse its angle with the angle from the vertical.
2. Compare with tangent without confusing their order
Where both are defined, COT(x)=1/TAN(x). =COT(RADIANS(60))*TAN(RADIANS(60)) should be approximately 1. For reliable formulas, avoid using this comparison close to either function’s singularities.
3. Handle negative values in quadrants II and IV
The cotangent of 150° is negative, because cosine is negative and sine positive. =COT(RADIANS(150)) has expected value −√3. A negative cotangent is often a legitimate sign of orientation, not a formula failure.
Errors, apparent surprises and safe troubleshooting
| Formula or symptom | Explanation and action |
|---|---|
=COT(0) |
Undefined in real mathematics because sine(0)=0. No exact runtime error code is confirmed in the ONLYOFFICE function page. |
=COT(PI()) |
Theoretical singularity at 180°; an approximation to π may yield a very large finite result. Do not rely on the displayed error/signed magnitude. |
=COT(30) when you mean 30° |
The function expects radians; use COT(RADIANS(30)). |
=COT(134217728) |
Outside the documented range: the vendor requires absolute argument strictly smaller than 2^27. The function page does not promise a specific error code; do not assert one. |
A quoted numeral ("1"), blank reference, logical TRUE or multiple arguments |
The one-argument vendor reference does not specify coercion or precise errors for these cases. Enter a genuine numeric value and check the real Desktop/web version instead of assuming behaviour from a different spreadsheet program. |
| Formula name appears unknown | Check the installed ONLYOFFICE editor version, Formula Language, and actual Function picker. A vendor’s current unversioned help article is not a guarantee about an old or custom-hosted installation. |
| Last decimal digits differ | Formatting, finite-precision π/radian conversion, argument reduction or transcendental evaluation can affect displayed digits. Use a tolerance rather than exact floating-point equality. |
A safer check for boundary-sensitive formulas
If your model will ever evaluate a mathematically singular point, test the domain before evaluation rather than relying on a specific error message or last-digit numerical coincidence. Avoid building critical logic around comparing COS(RADIANS(90)) or SIN(PI()) to exactly zero; floating-point values near the mathematical singularity need a numeric tolerance. This is mathematical design advice, not a verified ONLYOFFICE evaluation rule.
Related ONLYOFFICE references
- RADIANS — official ONLYOFFICE documentation (checked 2026-10-13 UTC).
- SIN — official ONLYOFFICE documentation (checked 2026-10-13 UTC).
- TAN — official ONLYOFFICE documentation (checked 2026-10-13 UTC).
Documentation and evidence classification (checked 2026-10-13 UTC)
- ONLYOFFICE function-page evidence: COT documents the displayed formula name, the one-argument signature, an input described as an angle in radians, and the magnitude restriction. It does not document native results for this article’s custom worksheet.
- Function entry workflow: ONLYOFFICE Docs: Inserting functions describes selecting Formula → Function, searching by name, and entering formulas with an equals sign. It gives English formula examples using commas as argument separators.
- Regional settings: Spreadsheet Editor Advanced Settings describes Formula Language, region, and decimal/thousands separators. Examples here use the English function name and decimal dot. Verify formula translation and separators in your installation rather than asserting a tested locale matrix.
- Product editions and versions: The ONLYOFFICE Docs changelog lists Docs 10.0.0, released 10 October 2026, whereas the Desktop Editors changelog separately lists Desktop Editors 9.4.0, released 19 May 2026. The official Desktop GitHub releases also lists 10.0.0 released 13 October 2026. These release references do not establish the first version supporting this function, nor prove Desktop/web runtime parity.
- Runtime confidence: Custom numerical expectations were independently recalculated at high precision. Native ONLYOFFICE Desktop/web execution and locale-specific parsing were not tested.
Native compatibility checks
For compatibility checks, record the named Docs web version and Desktop build, cell results, function availability, extreme-input behavior and relevant singular boundaries. Repeat with the formula language and regional settings actually used.