ACOSH in SoftMaker PlanMaker 2026: inverse hyperbolic cosine and input rules

Hyperbolic cosine COSH(t)=(e^t+e^(-t))/2 has values from 1 upward for real t. Because COSH(t)=COSH(-t), it cannot have a unique inverse across all real t. The standard real principal inverse, ACOSH(x) or arcosh(x), chooses the nonnegative solution for x≥1. Consequently, COSH(ACOSH(x))=x for every valid real input x, but ACOSH(COSH(t))=ABS(t) for arbitrary real t. The manufacturer’s documentation gives the positive example ACOSH(COSH(0.1234)) → 0.1234; it does not state that a negative original t would be restored with its sign. SoftMaker ACOSH · COSH; math principal-branch interpretation verified independently 2026-10-13.

Applications include reversing a catenary-style mathematical curve, recovering magnitudes from cosh-derived ratios and checking hyperbolic function identities. It is not an angle-measuring version of ACOS: PlanMaker’s ACOS documentation takes inputs from -1 to 1 and returns ordinary inverse cosine in radians, whereas ACOSH takes inputs ≥1 and yields a hyperbolic parameter. An ACOSH result does not ordinarily need degrees conversion.

=ACOSH(Number)

The 2026 and 2024 official references spell the function as ACOSH(Number) and identify it as the inverse of COSH. The terse PlanMaker function entry does not separately print an explicit >=1 sentence; that bound follows from the real mathematical definition, and Microsoft’s separate ACOSH description explicitly states the identical real-number domain for Excel. This is not evidence that a deliberately invalid PlanMaker call was executed. The first argument is not an angle in degrees, and there is no second argument or mode selector. PlanMaker 2026 ACOSH · 2024 ACOSH, checked 2026-10-13.

Enter the leading equals sign in worksheet cells; SoftMaker’s formula entry instructions require it. Because ACOSH has only one argument, the direct examples need no argument separator. The English manuals use decimal dots; localized decimal entry, coercion of numbers stored as text and internationalized function naming were not tested.

Enter each numeric input into A2:A9 as shown. In B2, type =ACOSH(A2) and fill down to B9. Apply a nine-decimal number format to column B. The numbers below were computed independently via Python’s math.acosh, not returned from a native PlanMaker formula execution.

All examples meet the mathematical domain restriction. The boundary case A2=1 produces 0. An input such as 0.999 is just below the boundary and has no real ACOSH value; treating it as a small positive answer is wrong. Note how input 100 maps to only about 5.298, a reminder that the inverse grows slowly for large ratios. The original manufacturer’s direct example =ACOSH(1.1) is predicted to be 0.443568254 and displayed in its documentation as 0.44357. SoftMaker PlanMaker ACOSH.

Recreate and interpret the manufacturer’s composition

Enter =ACOSH(COSH(0.1234)) in an empty cell. The official 2026 document displays 0.1234. Change the inner input to -0.1234:

=ACOSH(COSH(-0.1234))

The mathematical expectation remains +0.1234, not -0.1234, because COSH is even and ACOSH selects the nonnegative branch. This second composition is independently calculated; it is not a PlanMaker runtime observation. If the sign is important to your model, retain it in another cell rather than trying to recover it from COSH alone. ACOSH · COSH · ABS.

1. Invert a catenary-style relation without claiming an engineering design

For an idealized mathematical curve y = a*COSH(x/a), with positive scale a, a measured y requires y/a >= 1. The nonnegative horizontal distance magnitude is x_mag = a*ACOSH(y/a). Enter 4 into D2 (scale), 8 into E2 (ordinate) and enter:

=D2*ACOSH(E2/D2)

The independently expected magnitude is 5.267831588 in the same units as D2. The two symmetric x-positions are ±5.267831588; ACOSH does not determine which side of the curve a point occupies. Enter 3 into E2 while D2 remains 4: the ratio is 0.75, below 1, so there is no real result for this idealized equation. Before building a real physical model, check loads, supports, geometry and units independently; the formula is not an engineering-safety recommendation. Official ACOSH and COSH.

2. Validate the input using a formula that separates valid and invalid rows

With numeric A2, the following uses the PlanMaker 2026 IF syntax and a direct mathematical domain check:

=IF(A2<1,"OUTSIDE REAL DOMAIN",ACOSH(A2))

For A2=2, the expected numeric branch is 1.316957897. For A2=0.75, the expected branch is the text OUTSIDE REAL DOMAIN. This proposed combined formula was not executed in PlanMaker and assumes A2 is numeric. The example uses the documented English comma separator, while an installation’s locale can change accepted separators; consult the local function dialog if necessary. Do not assume an IF guard makes numeric text or an error-cell argument valid. IF syntax · ACOSH syntax; checked 2026-10-13.

3. Compare logarithmic and built-in forms at moderate magnitude

The mathematical identity for real x>=1 is acosh(x)=ln(x+sqrt(x*x-1)). With A2=3, compare =ACOSH(A2) with:

=LN(A2+(A2^2-1)^0.5)

Both are expected independently to be 1.762747174. This is a mathematical cross-check; PlanMaker 2026 LN documents the log function, and no native composed-formula result was observed. At x=1, the log expression gives LN(1)=0. For an input very close to 1, subtraction x^2-1 can be numerically delicate; using ACOSH directly is generally clearer. Exact PlanMaker floating-point precision and overflow thresholds are untested.

4. Check principal-branch symmetry explicitly

Put -2 in A2 and compare =ACOSH(COSH(A2)) with =ABS(A2). The independent expected value is 2 for both. Repeat with A2=+2 to confirm that the result remains 2. This demonstrates why a source model that depends on negative-versus-positive position must store a separate sign or orientation. The official PlanMaker functions are individually documented: COSH, ACOSH, ABS.

5. Inspect near-boundary sensitivity

For ε>0 very small, ACOSH(1+ε) is approximately SQRT(2*ε) in mathematics. Enter a numeric A2=1.000001 and compare =ACOSH(A2) against =(2*(A2-1))^0.5. The independent ACOSH prediction is 0.001414213444; the approximation is 0.001414213562. A small discrepancy is expected because the approximation neglects higher-order terms. Avoid applying it beyond the near-1 regime. Numeric equality for A2 values incredibly close to 1 depends on actual floating-point precision, which was not characterized for PlanMaker.

If an error cell is encountered, PlanMaker’s error-value reference explains the categories. There are zero native app tests in this package, so all rows above distinguish a documented general error classification from an actually observed PlanMaker ACOSH outcome.

Having the same documented mathematical function name is not proof that a PlanMaker workbook using ACOSH was imported by Excel or vice versa. In particular, Excel-specific error formatting or date/version applicability cannot stand in for PlanMaker runtime evidence.

• COSH (hyperbolic cosine): the function inverted by ACOSH; even around zero.
• ASINH (inverse hyperbolic sine): unlike ACOSH, accepts all real inputs mathematically and retains sign.
• ACOS (inverse ordinary cosine): takes -1 through +1 and returns a circular angle in radians.
• LN (natural logarithm): used in the logarithmic ACOSH identity.
• ABS (absolute value): interprets nonnegative principal-branch output.
• IF (conditional): optional example of flagging a bad domain before invoking ACOSH.
• PlanMaker 2024 error values: diagnostic categories.

Links checked 2026-10-13.