PlanMaker COTH: Hyperbolic Cotangent and Inverse 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.

=COTH(Number)

The argument is the input to the hyperbolic cotangent. It is not a circular angle that should automatically be converted from degrees. The NIST hyperbolic definitions give coth(x)=1/tanh(x)=cosh(x)/sinh(x). This is a different function from COT.

The official PlanMaker example is =COTH(0.45), reported as 2.37024. That is a rounded illustration. The higher-precision independent expectation is 2.3702355008.

The ordinary real function is undefined at zero. The checked manual does not specify the exact native error there or a detailed input/coercion range. The reproducible controls use strictly positive numeric values, avoiding that unresolved endpoint.

Create HyperbolicControls with Input in A1, Coth in B1 and Reciprocal_check in C1. Enter the values below in A2:A7. Fill B2 =COTH(A2) and C2 =1/TANH(A2) down.

On a copy change A5 from 1 to 2. Both row-5 expectations become 1.0373147207, matching the unchanged row 6. Increasing the positive input decreases coth toward one; it does not produce the periodic oscillation of an ordinary cotangent.

NIST’s definitions imply coth(x)=(exp(2x)+1)/(exp(2x)−1). In D2 enter =(EXP(2*A2)+1)/(EXP(2*A2)-1) and fill down. For these moderate positive inputs, its mathematical expectations match B and C.

This is a check on meaning, not a claim that all three native algorithms have identical accuracy. At large x, forming exp(2x) can overflow even when coth(x) is close to one. Near zero, subtracting one from a nearly-one exponential can lose relative precision. The direct function should not be replaced blindly by that algebraic identity in every numerical regime.

Put Excess_over_one in E1 and fill E2 =B2-1 down. For x=1,2,3, expected excesses are 0.3130352855,0.0373147207,0.0049698233. These positive values shrink as the argument grows.

A displayed value of 1 at limited precision does not mean the mathematical function equals one at a finite positive input. Keep enough digits or inspect the excess when that small difference is the quantity a model actually needs. Native cancellation and extreme-input accuracy are not established here.

The PlanMaker ACOTH reference identifies ACOTH as the inverse of COTH. Put F2 =ACOTH(B2) and fill through F7 using the original table. The mathematical target is the original A value in every row: 0.1,0.45,0.5,1,2,3.

This check stays within positive inputs and outputs greater than one. It is not a test of ACOTH’s behavior at ±1, zero or a complex branch. The vendor also gives the round trip ACOTH(COTH(0.1234)) as 0.1234. Preserve that finite positive control rather than generalizing its success to undocumented invalid inputs.

If a result differs from COT, verify which mathematical function the model calls for. The hyperbolic name does not authorize treating a measurement in degrees as its natural input. A dimensional model must define how its physical parameters become the dimensionless argument.

The reference does not establish exact errors or coercions for blank cells, arbitrary strings, arrays, zero or very large magnitudes. This guide makes no claims for those cases beyond the mathematical cautions above. Do not label an independent Python or high-precision calculation as a PlanMaker execution.

For native reproduction, record the build, edition, platform, language and workbook format. Recreate the original cells, compare the finite table first, and test any required small-difference accuracy separately. A correct inverse relation at ordinary values does not certify data transport or a model’s physical assumptions.