COTH in WPS Spreadsheet: Calculate Hyperbolic Cotangent Ratios
Calculate hyperbolic cotangent in WPS Spreadsheet and apply a shared scale and multiplier to a mathematical response column.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: COTH returns hyperbolic cotangent. =COTH(1) has independently calculated expectation 1.313035285.
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
=COTH(number)
One required numeric argument, number, supplies the hyperbolic input. In a scaled model, use a dimensionless ratio such as distance/scale. It is not the circular cotangent of an angle.
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: inspect a decreasing positive curve
Enter 0.5, 1 and 2 in A2:A4. Fill =COTH(A2) down B2:B4. Expected values are 2.163953414, 1.313035285 and 1.037314721. The positive curve approaches one as the input grows; it does not oscillate like a circular trigonometric function.
This small grid is useful for checking a hyperbolic formula in a mathematical model or demonstrating how rapidly the curve changes near zero. Keep zero out of this ordinary-input grid.
Example 2: apply a shared scale
Suppose a mathematical response is y=10*coth(x/2). Put x values 1, 2 and 4 in D2:D4, scale 2 in G1 and multiplier 10 in H1. Fill =$H$1*COTH(D2/$G$1) down E2:E4. Expected outputs are 21.639534137, 13.130352855 and 10.373147207. Fixed references preserve the scale and multiplier when copied.
The units of x and scale must match for their ratio to be dimensionless. Treat this as an explicitly defined mathematical response, not a validated engineering model.
Advanced checks: ratio and sign
For x=1, compare =COTH(1) with =COSH(1)/SINH(1). Both expectations are 1.313035285. The underlying definition is cosh(x)/sinh(x). A second moderate-input check is =(EXP(2)+1)/(EXP(2)-1), which yields the same expectation.
The mathematical function is odd: the expected result of =COTH(-1) is -1.313035285. A symmetric pair can expose a sign error in upstream data. These identities are ordinary-input mathematical controls, not assurances that alternative formulas behave identically at numerical extremes.
Troubleshooting and limits
- Do not substitute COT: the hyperbolic and circular functions describe different relationships.
- At zero, the mathematical denominator sinh(0) vanishes. The exact WPS error behavior at zero is not established by the reviewed source.
- A large positive result near zero can be mathematically expected. Check the input scale before labeling it a formula failure.
- WPS’s FAQ recommends checking numeric input for
#VALUE!. Text/blank coercion, overflow thresholds and an exhaustive error table remain unverified.