CSCH in Google Sheets: Use Reciprocal Hyperbolic Sine with Signed Inputs

• Introduced: first service launch date is not established by the official history reviewed; no numbered desktop introduction is assigned.
• Availability: documented in the rolling Google Sheets service. Examples use ordinary web-spreadsheet numeric cells; other clients and imported files are not separately certified.
• Checked: October 14, 2026; official CSCH reference. Documentation and independent calculations, without native Sheets execution.

=CSCH(value)

The argument is a real numeric model value. Mathematically CSCH is 1/SINH wherever the denominator is nonzero. The help’s broad real-input description should therefore be read with its zero-error example.

This hyperbolic function differs from circular CSC. Do not add a degrees-to-radians conversion to an arbitrary model quantity just because the function names resemble one another.

Enter −1.5, −0.75, 0.75, 1.5, 3 in A2:A6 and fill =CSCH(A2) down. Expected values are approximately −0.469642441, −1.216076435, 1.216076435, 0.469642441, 0.099821570.

Unlike circular cosecant, hyperbolic cosecant can have magnitude below one. Its sign follows the input. A negative source therefore should not be rejected merely because a positive geometric interpretation was assumed elsewhere.

=CSCH(LN(3))
=1/SINH(LN(3))

Both expected results are 0.75, because SINH(LN(3))=(3−1/3)/2=4/3. SINH is the forward reciprocal partner.

Keep LN(3) as a formula when reproducing the control. Retyping a shortened decimal changes the source precision before the comparison starts.

For a fictional model y=5*CSCH(x/3), put positive x values 1.5, 3, 6 in D2:D4. Use:

=5*CSCH(D2/3)

Expected responses are approximately 9.595173757, 4.254590641, 1.378602824. The decrease is nonlinear. Doubling x does not halve y in general.

The explicit input domain avoids zero and provides positive responses. Choosing this curve for measured data would require its own model justification; a spreadsheet formula does not supply that evidence.

If E2 holds the unrounded response, the inverse model is =3*ASINH(5/E2). Filled down, it is expected to reconstruct approximately 1.5, 3, 6.

ASINH preserves sign for real inputs. But a response rounded or underflowed to zero cannot be inverted through a reciprocal. Retaining the raw source is safer than assuming every transformed display can recover it.

The literal-zero #DIV/0! result is direct vendor evidence, separate from the independent numerical models above. Near zero the mathematical ratio can become very large, while at large input magnitudes it becomes small.

Expanding SINH into exponentials can create huge intermediate values even when the reciprocal is small. Do not interpret an algebraic identity as a guarantee of equal native stability.

Google’s reference does not establish Excel’s input-magnitude restriction or a complete coercion matrix. Keep those product-specific questions open and test the actual Sheets file when extreme values or imported types are part of the requirement.

• Google CSCH help.
• Editorial testing standards.

Inputs are fictional. Approximate numerical answers are independently calculated mathematical expectations rounded to nine places, not captured native results. Complete coercion, extreme-magnitude and cross-client behavior remain untested.