ACOT in Google Sheets: Positive Inputs, Degree Conversion and a Branch Warning

• 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 ACOT reference. Documentation and independent calculations, without native Sheets execution.

Google’s note states that results lie between zero and pi, but its example for input −4 prints a negative angle. Those claims cannot both describe the same principal branch. No native Sheets execution was performed to resolve the discrepancy.

Accordingly, this guide’s worked ACOT outputs use nonnegative inputs. Do not use it to certify an imported negative-input formula against Excel, Calc or another application. The conflicting source case is discussed below as a verification hold, not silently assigned one expected native answer.

=ACOT(value)

The required value is a numeric cotangent ratio. The result is in radians; multiply the result by 180/PI() for degrees. Converting the input ratio as if it were already a degree angle would change the problem.

Zero is included in Google’s explicit examples and yields approximately pi/2, or 90 degrees. A reciprocal shortcut that first divides by zero is therefore unsuitable for that valid control.

Put 0, 0.5, 1, 2, 5 in A2:A6. In B2 enter and fill down:

=ACOT(A2)*180/PI()

Expected angles are approximately 90, 63.434948823, 45, 26.565051177, 11.309932474 degrees. For strictly positive inputs, increasing the cotangent ratio decreases the acute angle.

Keep the raw ratio and radian inverse available if a later formula expects radians. A degree-converted display should not be passed directly into COT without converting it back.

For adjacent side 8 and opposite side 6 in a right triangle:

=ACOT(8/6)*180/PI()

Expected angle: approximately 36.869897646 degrees. The positive side lengths naturally select the acute solution. This example does not generalize to a full signed-coordinate direction.

For positive inputs 0.5, 1, 2, 5, =COT(ACOT(A2)) is expected to reconstruct the source ratio within ordinary tolerance. COT receives the radian result directly.

For these positive inputs, ATAN(1/value) agrees mathematically with the acute ACOT angle. That agreement does not resolve the negative branch, and the reciprocal expression fails at zero.

For input −4, the source’s printed answer is approximately −0.244978663 radians, or −14.036243468 degrees. A branch confined to zero through pi would instead select approximately 2.896613990 radians, or 165.963756532 degrees. Both angles have cotangent −4, but they are different branch choices.

These are the two mathematical interpretations of conflicting documentation, not two native results measured in Sheets. Test negative inputs in the intended file before adopting either interpretation. Keep source coordinates and consider ATAN2 when direction, rather than a chosen inverse ratio branch, is the real requirement.

• Google ACOT 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.