ACOT in Collabora Office: Return the Principal Inverse Cotangent Angle

• Introduced: original Collabora release and launch date are not established by the sources reviewed.
• Availability: documented in Collabora Office 26.04 help, scoped to the desktop-help release.
• Platform scope: support in every online or mobile deployment is not inferred from desktop documentation.
• Checked: October 14, 2026. Direct function-specific documentation and independent numerical examples; no native Collabora test was performed.

=ACOT(number)

number is a cotangent value, not an input angle in degrees. Collabora documents an output between 0 and PI and recommends DEGREES when a degree result is wanted.

This branch convention matters for negative inputs. It differs from blindly calculating ATAN(1/number), which can select a different principal angle and introduces a division problem at zero. Do not substitute that expression without checking the branch and domain.

The examples use English function names and standard arithmetic operators. Decimal results are rounded independent expectations; exact stored equality has not been certified in a native application.

=ACOT(1)
=DEGREES(ACOT(1))
=DEGREES(ACOT(0))
=DEGREES(ACOT(-1))

Expected results: approximately 0.785398163 radians, 45 degrees, 90 degrees, 135 degrees. Zero is a valid cotangent value on this inverse branch and corresponds to a right angle.

A negative cotangent therefore does not imply a negative ACOT result. The selected angle is in the second quadrant under this convention. DEGREES converts the output unit without changing the branch.

=DEGREES(ACOT(SQRT(3)))
=DEGREES(ACOT(1/SQRT(3)))

Expected results: approximately 30 and 60 degrees. Cotangent is adjacent divided by opposite in an acute right triangle, so a larger positive ratio corresponds to a smaller acute angle.

These examples use positive ratios. Do not apply the triangle interpretation as though a negative algebraic ratio were a positive physical side length. Signed circular functions encode directional information beyond the elementary length ratio.

=DEGREES(ACOT(-1))
=DEGREES(ATAN(1/(-1)))

Expected results: 135 and −45 degrees. Their cotangents agree because the angles differ by 180 degrees, but their numerical angles are not identical.

ATAN has its own principal range. For an actual direction specified by signed horizontal and vertical coordinates, ATAN2 can preserve quadrant information using both coordinates. A single ratio cannot distinguish every full-circle direction.

For degree inputs 45, 135 and 225, compare the original angle with:

=DEGREES(ACOT(COT(RADIANS(A2))))

Expected recovered degrees: 45, 135, 45. The 225-degree case has the same cotangent as 45 degrees, so ACOT returns the principal representative rather than the original full-turn history.

This example depends on the documented circular cotangent relationship and its periodicity. Preserve the original angle or extra quadrant information when reconstructing an orientation is part of the task.

Suppose an illustrative right triangle has adjacent length 8 and opposite length 6. Use:

=DEGREES(ACOT(8/6))

Expected result: approximately 36.869897646 degrees. A forward check with =COT(ACOT(8/6)) should reconstruct approximately 1.333333333.

Both lengths are positive in this example, placing the chosen angle in the acute range. The formula does not validate a measured triangle or decide whether a physical model is appropriate. Keep the input quantities and their units beside the ratio.

The inverse ACOT has an ordinary value at zero, but its forward partner COT is mathematically undefined at integer multiples of π. Do not expect every possible angle to pass through a forward/inverse composition safely.

Very large positive or negative cotangent values approach the ends of the principal angle range. Numerical rounding can make an output look like an endpoint even when the ideal finite-input angle is inside the range. This guide does not benchmark extreme magnitudes or every native error code.

Check whether your input is a cotangent ratio or an angle. Convert the result with DEGREES when needed; do not convert the input ratio with RADIANS. If a negative input produces a positive angle, compare that behavior with the documented branch before treating it as an error.

Use controls at 1, 0 and −1 to verify branch conventions when transferring formulas between products. Identical function names do not establish identical inverse-angle conventions without product-specific evidence.

• Collabora Office 26.04: ACOT.
• Editorial testing standards.

The official section supplies the product-specific definition and documented domain or angle branch. Original worked values were independently calculated. Native execution, extreme-value benchmarks and broader client compatibility remain unverified.