TANH in WPS Spreadsheet: Calculate a Bounded Hyperbolic Response

• Introduced: documented by 2019-06-25 in the official WPS lesson; original introduction is not established.
• Availability: WPS Office for Windows Personal; no numeric release is stated in the edition metadata.
• Scope: exact current supported builds remain unverified. The Windows lesson does not establish equivalent availability in other WPS clients.
• Checked: October 14, 2026 against function-specific documentation. Examples were independently calculated; no native WPS test was performed.

=TANH(number)

WPS documents one real-number input. TANH is hyperbolic, not the circular tangent of a degree or radian angle. Do not insert a degree-to-radian conversion unless the surrounding model specifically defines that transformation.

The lesson’s walkthrough mentions #VALUE! for a non-real argument, but it does not define every spreadsheet string, blank or logical-value conversion. That prose is not treated as a complete native type-test matrix.

Enter −2, −1, 0, 1 and 2 in A2:A6 and fill =TANH(A2) down:

Negating the input negates the output. Increasing a positive input moves the result toward one, but the mathematical function does not exceed one. Exact native last digits or the point at which a finite-precision implementation rounds to one are not measured here.

For input one:

=TANH(1)
=SINH(1)/COSH(1)

Both expected values are approximately 0.761594156. The mathematical ratio uses hyperbolic sine divided by hyperbolic cosine. The latter is positive for real inputs, so there is no ordinary real-input zero denominator in this identity.

For this modest input, (EXP(2)-1)/(EXP(2)+1) is another equivalent control. It is not a universally stable replacement for TANH at very large magnitudes.

Define a fictional response by 50+30*tanh(x/2). The intended mathematical lower and upper limits are 20 and 80, with midpoint 50. Enter −4, −2, 0, 2 and 4 in D2:D6:

=50+30*TANH(D2/2)

Expected outputs are approximately 21.079172598, 27.152175321, 50, 72.847824679 and 78.920827402. All lie between the two limits. The input division sets the transition scale, while the outside multiplier and offset set the output scale.

Those limits are approached, not reached at a finite real x in the exact model. If a rounded display shows 80, it does not by itself prove that the mathematical output equals 80.

For the same response, choose target y=65. Rearrangement gives tanh(x/2)=(65−50)/30=0.5:

=2*ATANH((65-50)/30)

Expected x: approximately 1.098612289. Substituting it into 50+30*TANH(x/2) returns 65 mathematically. Target 35 gives the opposite x, approximately −1.098612289.

Targets exactly 20 or 80 would require ATANH of −1 or 1, outside its documented open domain. Values beyond the limits are also not solved by this real-valued model. See ATANH for the inverse restriction.

For x=0.1, TANH has expected value approximately 0.099667995. The simple approximation x−x³/3 is 0.099666667, differing by about 0.000001328.

The approximation is useful for understanding local behavior near zero, but its closeness at 0.1 is not evidence of accuracy for arbitrary inputs. Retain the actual function for the documented computation.

Keep unrounded results for inverse checks. Rounding a TANH result to an endpoint before applying ATANH changes a valid interior input into an invalid one. No native saturation threshold or overflow rule is certified.

Compare SINH and COSH when a model requires unbounded hyperbolic components rather than a bounded ratio. The historical Windows lesson does not establish every current WPS client’s implementation details.

• WPS Academy: TANH lesson, 2019-06-25 (Chinese; Windows Personal scope).
• Editorial testing standards.

The direct WPS product lesson supports the stated function scope. Worked outputs are independent expectations, not captured native results or proof of support across all current WPS clients.