PlanMaker COT: Radians, Cotangent Tables and Unit Checks

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.

=COT(Number)

Number is an angle in radians. For a degree value in A2, use =COT(RADIANS(A2)) or =COT(A2*PI()/180). The manual explicitly recommends RADIANS for conversion. Typing =COT(45) asks for 45 radians, not a 45-degree angle.

Mathematically cot(x)=cos(x)/sin(x). It is the reciprocal of tangent where that relationship is defined. This guide uses finite angles away from singularities and does not assign a native result or error token at zero or integer multiples of π.

The two official controls, =COT(PI()/4) and =COT(RADIANS(45)), both return 1. Their equivalence is a useful unit check, not evidence that arbitrary degree values can be passed without conversion.

Create AngleControls with Degrees in A1, Radians in B1 and Cotangent in C1. Enter the degree values below in A2:A7. Fill B2 =RADIANS(A2) and C2 =COT(B2) through row 7.

In a copy change A3 from 30 to 45. B3 becomes approximately 0.7853981634 and C3 becomes 1. Row 4 already contains the unchanged 45-degree control, so both rows should agree mathematically.

Positive and negative outputs reflect the angle’s quadrant. The 120- and 135-degree controls are not negative inputs; they are angles with negative cotangents. A blanket expectation that all positive angles have positive results would be wrong.

For a purely geometric example, fix an opposite side of 3 units. Enter acute angles 30,45,60 degrees in F2:F4 and fill G2 =3*COT(RADIANS(F2)) down. Expected adjacent lengths are 5.1961524227,3,1.7320508076.

The opposite side stays fixed while the angle increases, so the adjacent side decreases. If the 30-degree input changes to 45, its expected adjacent side becomes 3. This is an ideal mathematical construction, not a survey or structural-design validation; measurements and tolerances are separate concerns.

On the original AngleControls sheet, D2 =COS(B2)/SIN(B2) provides the same mathematical result as C2. Fill down to compare the two formulations on the nonsingular inputs. Use underlying cell values rather than recomputing from the rounded radian column printed here.

Cotangent repeats after π radians. A fresh control =COT(RADIANS(30)+PI()) has expected value 1.7320508076, matching 30 degrees rather than changing sign. Adding a full π differs from changing the sign of the angle: cot(−x)=−cot(x) mathematically.

For small positive radian inputs, =COT(0.01) is approximately 99.9966666444, while =COT(0.001) is approximately 999.9996666666. These are finite controls, not an evaluation at zero. Their large values illustrate why a small angular perturbation near a singularity can create a large output change.

The simple estimate 1/x is close for these small inputs but is not the exact definition. Replacing COT with that approximation for all angles would fail even at π/4, where the function is one.

The short PlanMaker reference does not give a complete error table for singularities, excessive argument magnitudes, text, blanks or arrays. No exact native error is invented for those cases. Mathematical undefinedness and a particular program’s error token are different claims.

Check degree/radian conversion first when a familiar angle produces an unexpected answer. Near an exact multiple of π, finite representations of PI and arithmetic rounding can complicate an intended singular test. Record the installed version, language and workbook format and reproduce the ordinary controls before extending them to sensitive numerical cases.