ACOTH in WPS Spreadsheet: Invert a Hyperbolic Cotangent Model
Use ACOTH in WPS Spreadsheet to invert positive hyperbolic cotangent values above one and solve a scaled mathematical model.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: ACOTH returns inverse hyperbolic cotangent. The ordinary control =ACOTH(2) has independently calculated expectation 0.549306144.
Availability and evidence scope
The official WPS Windows pages, checked October 19, 2026, document this function and advertise ordinary entry and calculation without membership. Their last-updated date is 2026-07-07; that is a documentation date, not its introduction release. They do not name an exact minimum or last supported build. Availability on Mac, Linux, mobile, web or historical builds is not established here.
The examples below are independently calculated mathematical expectations, rounded to nine decimal places where appropriate. They were not executed in WPS, and no native screenshot is claimed. Before relying on an installation, check its function prompt and run a small control example.
Syntax and arguments
=ACOTH(number)
One required numeric argument, number, is the hyperbolic cotangent value to invert. It is not an ordinary angle in degrees. The worked examples use positive values comfortably above one.
The documented Windows workflow supports typing the formula in a cell or choosing the function through Formula → Insert Function. These formulas use English names and comma separators. Inspect the destination formula after filling down so that relative references and fixed settings still point to the intended cells.
Example 1: invert a small input series
Enter 1.5, 2 and 3 in A2:A4. Fill =ACOTH(A2) down B2:B4. The mathematical expected values are 0.804718956, 0.549306144 and 0.346573590. The inverse decreases across these positive inputs; an increasing result is a reason to check that the intended function and cells were used.
These values can serve as a compact regression worksheet when transferring an existing hyperbolic model to a different installation. Record the actual WPS build alongside any results you observe; this guide does not supply a native execution record.
Example 2: solve a scaled model
A mathematical model defines r=coth(t/4). If r=2, solve t=4*acoth(r). Put 2 in D2 and scale 4 in E2, then enter =E2*ACOTH(D2). The expected t is 2.197224577 in the same units as the scale. The ratio t/4 is dimensionless. The worksheet solves the stated equation; it does not establish that this equation describes a particular physical system.
Advanced check: a logarithmic derivation
For the selected real inputs greater than one, acoth(x)=0.5*ln((x+1)/(x-1)). With A2=2, compare =ACOTH(A2) with =0.5*LN((A2+1)/(A2-1)). Both expectations are 0.549306144. This checks the meaning independently of a second inverse-hyperbolic implementation.
An optional forward check for B2 is =(EXP(2*B2)+1)/(EXP(2*B2)-1), whose expectation is the original A2. Use only these modest test values: algebraically equivalent formulas can have different overflow and cancellation behavior.
Troubleshooting and limits
- Check that the input is the model’s output r, not its parameter t. ACOTH and COTH perform different operations.
- Near one, the real mathematical inverse changes rapidly. Do not round a measured ratio to one before evaluating a model that requires more precision.
- For the real logarithmic definition, values with absolute value above one give a real inverse. This mathematical observation is not a tested statement of WPS error behavior at or inside the boundary.
- WPS-specific documentation does not establish the exact invalid-input error code, numeric bounds, or text/blank coercion rules. Its Excel comparison cannot supply that missing contract.