SECH in Collabora Office: Build Hyperbolic Secant Calculations and Curves

• Introduced: original Collabora release and launch date are not established by the sources reviewed.
• Availability: documented in Collabora Office 26.04 help, scoped to the desktop-help release.
• Platform scope: support in every online or mobile deployment is not inferred from desktop documentation.
• Checked: October 14, 2026. Function-specific documentation and independent numerical examples; no native Collabora test was performed.

=SECH(number)

number is the hyperbolic argument. Mathematically, SECH(x)=1/COSH(x), with COSH providing the related hyperbolic cosine. The real function is defined at zero and at ordinary positive or negative finite inputs.

SECH is not the inverse hyperbolic cosine ACOSH. A reciprocal returns one divided by a function value; an inverse asks which original argument produced a value.

Do not automatically convert the input with RADIANS. The model should define the hyperbolic argument and any required dimensionless scaling.

Enter −2, −1, 0, 1, 2 in A2:A6. In B2 enter and fill down:

=SECH(A2)

The function is even, so opposite inputs return equal values. Its mathematical real output is positive and no greater than one, with the peak at zero. As the magnitude of the input grows, the mathematical value tends toward zero.

This mathematical range does not guarantee that an extreme finite-precision calculation cannot underflow to a stored zero. The table uses ordinary inputs well away from such a benchmark question.

=SECH(1)
=1/COSH(1)
=SECH(1)*COSH(1)

Expected results, approximately: 0.648054274, 0.648054274 and 1. Use full calculated values rather than manually rounded decimal strings for the product.

For a zero-input control, =SECH(0) returns the mathematical value one, because COSH(0)=1. This is different from CSCH and COTH, whose reciprocal relationships involve SINH(0)=0.

Consider the illustrative curve 100*SECH(x/2). Put −4, −2, 0, 2, 4 in A2:A6. Enter in B2 and fill down:

=100*SECH(A2/2)

The multiplier 100 controls the peak height. The divisor 2 controls the horizontal scale. They are separate parameters, so changing one is not equivalent to changing the other.

The table can be used as input to a scatter chart, keeping x as a numeric horizontal axis. It is an illustrative mathematical shape, not a claim that these parameters fit a particular measured dataset. If x has units, its scale should have matching units so x/2 represents the intended dimensionless argument.

For the curve above, half height means SECH(x/2)=0.5. Rearranging gives COSH(x/2)=2. The positive position is:

=2*ACOSH(2)

Expected result: approximately 2.633915794. By symmetry, the negative position is approximately −2.633915794. The distance between these positions is approximately 5.267831588.

For a forward check, =100*SECH(ACOSH(2)) is expected to return approximately 50. The argument is ACOSH(2) because the positive position already contains the scale factor 2, which the model divides out.

ACOSH returns a nonnegative principal value. Include the negative position separately when a symmetric curve requires both sides; a one-sided inverse does not preserve the original sign.

=TANH(1)^2+SECH(1)^2

Expected result: approximately 1. TANH and SECH satisfy this identity mathematically. Small floating-point differences can remain when each term is computed independently.

Do not replace the dedicated function with a manually expanded exponential expression and assume identical stability for extreme values. The direct function definition supports ordinary identities, while overflow, underflow, text coercions and exact native error displays need separate application tests.

No native Collabora extreme-value benchmark was performed for this guide. Preserve the original inputs and full stored precision when using inverse checks or comparing a calculated curve with measurements.

• Collabora Office 26.04: SECH.
• Editorial testing standards.

The official section supplies the product-specific definition and angle-unit guidance where applicable. Worked models, identities and rounded outputs are independently calculated expectations. Native execution and broader client compatibility remain unverified.