PlanMaker ACOTH: Inverse Hyperbolic Cotangent and Domain 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.

=ACOTH(Number)

PlanMaker defines ACOTH as the inverse of COTH: it returns the value whose hyperbolic cotangent equals Number. The source’s example =ACOTH(2) is approximately 0.54931, and =ACOTH(COTH(0.1234)) returns 0.1234.

This is a hyperbolic inverse, not a circular angle needing degree conversion. For the Number > 1 controls in this guide, its mathematical value is one half of the natural logarithm of (Number+1)/(Number−1). The NIST inverse-hyperbolic reference relates arccoth to arctanh(1/Number); on this real domain that gives the same logarithmic expression.

The real mathematical function also has a branch for inputs less than −1, but the short PlanMaker entry does not state a complete input/error policy. The examples deliberately stay above one. No native behavior at ±1, between −1 and 1, or for complex arguments is inferred from the broader mathematical definition.

Create InverseHyperbolic with Input in A1, Acoth in B1 and Log_check in C1. Enter the values below in A2:A7. Fill B2 =ACOTH(A2) and C2 =LN((A2+1)/(A2-1))/2 through row 7.

In a copy change A5 from 2 to 3. Its expected value becomes 0.3465735903, matching row 6. The independent value for input 2 is 0.5493061443, which explains the manual’s shorter 0.54931 display.

The two formulas represent the same mathematical value on the stated domain, but no identical native last-bit behavior is promised. Preserve the original cells and compare with a tolerance appropriate to the workbook’s task.

Put Reconstructed_input in D1 and fill D2 =COTH(B2) through row 7. The mathematical targets are 1.1,1.25,1.5,2,3,10, recovering the original A values. This confirms that ACOTH is an inverse function rather than a reciprocal operation.

For example, =1/COTH(2) is mathematically tanh(2), approximately 0.9640275801. It is not ACOTH(2), approximately 0.5493061443. Similar-looking function names do not make taking a reciprocal and taking an inverse interchangeable operations.

Consider the purely mathematical equation coth(2t)=3 with positive t. Put target 3 in F2 and multiplier 2 in G2. H2 =ACOTH(F2)/G2 has expected result 0.1732867951. I2 =COTH(G2*H2) reconstructs 3.

If the target changes to 2, H2 becomes 0.2746530722, and I2 reconstructs 2. The division by G2 solves the scaling in the argument; it is not a unit conversion to degrees. A physical model must define what t and its multiplier mean before this algebra is applied to measurements.

Inputs just above one correspond to larger inverse values. =ACOTH(1.01) is approximately 2.6516524540, and =ACOTH(1.001) is approximately 3.8007011673. Both are valid finite mathematical controls above the endpoint, not evaluations at one itself.

If a preceding calculation rounds a target down to exactly one, the original problem changes materially. Keep sufficient precision and inspect the underlying value rather than treating the displayed target as an exact input. The natural-log rearrangement can be sensitive to subtraction near that boundary.

The checked PlanMaker description does not name an exact native error for out-of-domain targets, malformed text, blanks, arrays or extreme inputs. Mathematical divergence at an endpoint is not evidence of a particular spreadsheet error code. The guide leaves those behaviors unverified.

Check that the target is a COTH output rather than a degree measurement or an ordinary cotangent. Then verify the input remains strictly above one for these fixtures. Record the PlanMaker build, language and workbook format during native reproduction; a high-precision inverse calculation alone does not certify import coercion, numerical limits or cross-product branch compatibility.