COT in Google Sheets: Calculate Cotangent and Recover a Horizontal Run

• Introduced: first service launch date is not established by the official history reviewed; no numbered desktop introduction is assigned.
• Availability: documented in the rolling Google Sheets service. Examples use ordinary web-spreadsheet numeric cells; other clients and imported files are not separately certified.
• Checked: October 14, 2026; official COT reference. Documentation and independent calculations, without native Sheets execution.

=COT(angle)

The required input is in radians. Multiply a degree value by PI()/180 or use RADIANS before calling COT. A cell format containing a degree sign does not alter the stored unit.

Cotangent is mathematically COS(angle)/SIN(angle) wherever that ratio is defined. It is a returned ratio, not an inverse angle. The Google page does not establish Excel’s 2^27 limit, so that product-specific restriction is not imported here.

Enter 15, 30, 45, 135, −30 degrees in A2:A6 and fill =COT(A2*PI()/180) down. Expected outputs are approximately 3.732050808, 1.732050808, 1, −1, −1.732050808.

Values above one and negative values can both be correct. A ratio does not retain the source’s complete turn count or circular position; cotangent repeats after a half-turn.

For a stated right triangle with vertical rise 8 and angle 25 degrees above horizontal:

=8*COT(25*PI()/180)

Expected horizontal run: approximately 17.156055364. The eight is the opposite side, not the hypotenuse. Cotangent multiplies an opposite side into its corresponding adjacent side.

Reference the unrounded run in a forward check using TAN of the same radian angle. The expected reconstructed rise is 8. Retyping a shortened display can introduce avoidable error.

At 30 degrees, =1/TAN(30*PI()/180) and =COS(30*PI()/180)/SIN(30*PI()/180) both give approximately 1.732050808. TAN is the ordinary reciprocal partner on valid finite inputs.

At 90 degrees, cotangent is mathematically zero while tangent is undefined. A reciprocal-TAN rewrite introduces an unsuitable intermediate at that exact angle, even though a finite numerical approximation may produce a tiny ratio.

COT at 45 and 225 degrees is expected to give approximately 1 in both cases. The equal result does not mean those two directions are identical. Keep the source angle whenever quadrant or phase matters.

ACOT returns an inverse branch, but its current Google help has conflicting negative-input examples. Do not use an unverified inverse branch as a universal round-trip certification.

The literal-zero error is directly documented. Mathematically all integer multiples of pi are singular because sine is zero. A PI()-constructed multiple is represented approximately, so another singular-looking formula may produce a huge finite value rather than the same observed error code.

Separate documented native examples from mathematical limits. Inspect unit conversion, angle source and proximity to a singularity before replacing an unexpected result with a fallback. No arbitrary coercion, magnitude-limit or client-wide precision guarantee is claimed.

• Google COT help.
• Editorial testing standards.

Inputs are fictional. Approximate numerical answers are independently calculated mathematical expectations rounded to nine places, not captured native results. Complete coercion, extreme-magnitude and cross-client behavior remain untested.