ACOSH in WPS Spreadsheet: Invert Hyperbolic Cosine Without Losing the Branch

• Introduced: documented by 2019-06-21 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.

=ACOSH(number)

Both the formal WPS definition and the walkthrough require a real input greater than or equal to one. The lesson also states an unrestricted ACOSH(COSH(x))=x identity. That statement needs a branch qualification: COSH has equal values at x and −x.

For the ordinary nonnegative principal inverse, the mathematically complete composition is ACOSH(COSH(x))=ABS(x). The examples below expose the sign distinction rather than repeating the unrestricted source sentence. This is mathematical reasoning, not a native negative-input composition test.

Enter 1, 1.5, 2, 3 and 10 in A2:A6 and fill =ACOSH(A2) down:

The domain includes one, whose inverse is zero. Zero is a valid output but not an allowed input under the documented real-domain requirement. Keep those roles distinct when validating data.

=COSH(ACOSH(3))

The expected mathematical result is 3. ACOSH first finds the nonnegative value approximately 1.762747174; COSH maps that value back to the input.

A reconstruction based on the unrounded formula result is preferable to typing a shortened table value. Native final-digit agreement and extreme-magnitude stability have not been measured.

Let a fictional model require cosh(x/2)=3. The principal solution is:

=2*ACOSH(3)

Expected x: approximately 3.525494348. Because COSH is even, the negative counterpart −3.525494348 also satisfies the original equation mathematically.

One ACOSH call returns the principal branch, not a list of both roots. Whether the negative counterpart belongs in a real application depends on the model’s permitted x values. A distance-from-center model might use both positions, while a nonnegative magnitude might use only one.

For inputs 2 and −2, both COSH results are approximately 3.762195691. Therefore a function of only that shared output cannot know which sign was supplied originally.

=ACOSH(COSH(2))
=ACOSH(COSH(-2))

The principal-branch mathematical expectations are 2 and 2. The second is the counterexample to the lesson’s unrestricted composition sentence. Preserve the original sign separately if a later computation needs it.

These statements explain the inverse’s meaning. They do not certify an untested native rounding policy or erase the explicitly noted source defect.

For input two:

=LN(2+SQRT(2^2-1))

Expected result: approximately 1.316957897, matching ACOSH(2). The square-root term is √3 and its argument is nonnegative because the selected input lies in the real domain.

This identity is useful for a modest independent control. It is not a universal numerical replacement near one or at extreme magnitudes, where cancellation, overflow or other precision effects need separate analysis.

Inputs such as 0.5, zero or −2 are outside the documented real domain. The selected lesson does not establish a specific displayed error for every such input, so this guide does not borrow an error code from Excel or another product.

Use explicit numeric input validation and keep the source values rather than replacing every failed calculation with zero. A zero inverse means the original valid input was one; it should not become a generic label for invalid data.

Compare COSH for the forward function and ASINH for an inverse with a different formal domain. Historical Windows evidence does not establish every current WPS client’s support or coercion behavior.

• WPS Academy: ACOSH lesson, 2019-06-21 (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.