PlanMaker ACOT: Positive Ratios, Radian Results and Branch Limits

The PlanMaker 2026 manual, 2024 manual and 2021 manual were retrieved on October 15, 2026. They establish documented support in those manual families, not an original introduction or a last-working-version endpoint. Both historical endpoints remain unverified. Every individual desktop build and FreeOffice/mobile edition is outside this check.

No native PlanMaker execution was performed. Numerical expectations are independent high-precision mathematical calculations, not captured application results. English formulas use commas; verify names and separators in the installed language and locale. Displayed decimals are rounded reference values, not a promise of native last-bit accuracy.

The manuals state that Microsoft Excel supports this function from Excel 2013 onward. That compatibility note is about Excel, not the introduction date of the PlanMaker function. It does not establish identical errors, coercion or numerical behavior in the two products.

=ACOT(Number)

Number is a cotangent value. ACOT returns an angle whose cotangent is that value, with the answer in radians. The manual recommends DEGREES for a degree display. The input is not itself an angle in degrees, so applying RADIANS to a cotangent ratio before ACOT would change the problem.

The official example =ACOT(1) is shown as 0.7854, or 45 degrees. The radian value is a rounded π/4. The source also gives =ACOT(COT(0.1234)) as 0.1234.

The checked reference does not state the complete principal-value interval or a detailed negative/zero-input branch policy. This guide therefore restricts the numerical table to positive input ratios, with expected angles between zero and π/2. It does not copy another spreadsheet’s negative-input branch convention.

Create InverseCotangent with Ratio in A1, Radians in B1 and Degrees in C1. Enter these positive ratios in A2:A7. Fill B2 =ACOT(A2) and C2 =DEGREES(B2) down.

In a copy change A5 from 2 to 1. B5 becomes approximately 0.7853981634 and C5 becomes 45, matching the original row 4. The larger positive ratio corresponds to a smaller acute angle, not a larger one.

A radian result such as 0.4636476090 is not 0.4636476090 degrees. Keep the two output columns explicitly labeled, and do not apply a degree symbol to an unconverted radian number.

For positive adjacent and opposite sides, their ratio is the cotangent of the acute angle measured beside the adjacent side. On TriangleRatios, put adjacent 4 in F2 and opposite 3 in G2. H2 =ACOT(F2/G2) has expected value 0.6435011088 radians. I2 =DEGREES(H2) is approximately 36.8698976458 degrees.

Changing the adjacent side to 3 while keeping the opposite side at 3 gives ratio one and angle 45 degrees. The model assumes a right triangle with positive sides. It does not infer a survey bearing or resolve quadrants for signed Cartesian coordinates.

On the original InverseCotangent sheet fill D2 =COT(B2) down. The mathematical targets are the original ratios 0.25,0.5,1,2,4,10. This is a useful column-by-column check that the angle output was fed back in radians.

For these positive inputs only, =ATAN(1/A2) is another mathematical formulation of the same acute angle. It does not establish that this expression is interchangeable with ACOT for negative or zero arguments. An inverse of a periodic function needs a branch convention before unrestricted equivalence can be claimed.

COT repeats after π, so the same cotangent value belongs to infinitely many circular angles. A ratio alone cannot reveal how many half-turns preceded it. The vendor’s positive round trip at 0.1234 radians lies in an ordinary acute region and is consistent with the examples here.

Do not infer that ACOT(COT(x)) must reproduce every original x. A workbook that needs a full orientation or rotation history must retain more information than a single cotangent value. This guide deliberately does not manufacture a complete PlanMaker branch table from one published round trip.

The short reference supplies neither a complete native error table nor explicit coercion rules for text, blanks and arrays. Its exact behavior at zero, on negative inputs or for extreme finite magnitudes was not native-tested. No additional error token or branch endpoint is asserted here.

When a result looks wrong, check whether the input was a ratio or an angle, whether the output is in radians or degrees, and whether a different inverse branch was assumed. Reproduce the fully specified positive controls in the actual PlanMaker build before extending the calculation to signed directions or sensitive numerical work.