COSH in Collabora Office: Evaluate Hyperbolic Cosine and Symmetric Curves

• Introduced: documented in Collabora Office 26.04 Help; the original introduction version is not established by the reviewed history.
• Availability: the official COSH reference documents support in Calc’s 26.04 desktop manual.
• Scope: this evidence does not establish identical behavior in Collabora Online, mobile clients or older releases.
• Checked: October 14, 2026 against the captured 26.04 manual. Examples were calculated independently; no native Collabora execution was performed.

=COSH(number)

The mathematical identity behind hyperbolic cosine is:

cosh(x) = (exp(x)+exp(-x))/2

The Collabora help identifies COSH as hyperbolic cosine and documents its zero-input value. The definition provides an independent way to calculate the examples. It does not make COSH interchangeable with COS.

Use the dimensionless input specified by the model. Automatically converting a number with RADIANS merely because the function name contains COS changes the mathematical problem.

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

=COSH(A2)

Expected B2:B6: approximately 3.762195691, 1.543080635, 1, 1.543080635, 3.762195691.

The results at positive and negative inputs are equal. Hyperbolic cosine is an even function: cosh(−x) = cosh(x). The minimum of one occurs at zero for real inputs.

This symmetry means the output does not preserve the sign of the original input. Do not expect a later inverse operation to recover whether x was positive or negative without other information.

Put 1 in D2 and compare:

=COSH(D2)
=(EXP(D2)+EXP(-D2))/2

Expected result for both: approximately 1.543080635. The two exponential terms are about 2.718281828 and 0.367879441; their mean gives the hyperbolic cosine.

EXP is useful for checking the definition at moderate values. A manually expanded expression is not necessarily the numerically best implementation for every input, so do not assume identical rounding or overflow behavior at extremes.

=COSH(LN(2))

Expected result: approximately 1.25. Substituting the exponential values 2 and 1/2 gives (2+1/2)/2 = 5/4.

For =4*COSH(LN(2)), the expected result is approximately 5. This supplies a useful cross-check that does not depend on memorizing a long decimal result. LN means the natural logarithm, not LOG10.

Consider the illustrative function:

=2*COSH(A2/2)

For inputs −2, 0, 2, expected results are approximately 3.086161270, 2, 3.086161270. Dividing the input by two changes the horizontal scale; multiplying the output by two changes the vertical scale.

This is a mathematical plotting example. Although hyperbolic-cosine curves occur in some physical models, the formula by itself is not a verified engineering model or a safety calculation.

To make the curve’s minimum zero for a display:

=2*(COSH(A2/2)-1)

For the same three inputs, expected outputs are approximately 1.086161270, 0, 1.086161270. Subtracting one occurs before the outer factor of two. Moving parentheses changes the vertical offset.

=COSH(1)^2-SINH(1)^2

Expected result: approximately 1. The identity uses subtraction, unlike SIN²+COS² for circular functions. SINH supplies the corresponding hyperbolic sine.

For large inputs, both squared terms can be enormous and close in relative magnitude. Subtracting them may lose significant digits. Use this identity as a moderate-input illustration rather than an unrestricted numerical accuracy guarantee.

COSH is not bounded above by one. A result such as 3.7622 at input 2 is valid and does not mean cosine has exceeded its range; it is a different function.

Large magnitudes grow rapidly and may exceed the numeric capacity of the installed application. This guide does not claim an exact overflow threshold or native error code. For tiny inputs, subtracting one from COSH can lose small differences through rounding, so precision-sensitive models deserve a separate numerical analysis.

Test the zero input and a positive/negative pair, retain enough calculation precision and label any scaling parameters. A rounded display should not be treated as proof of exact equality in a longer calculation chain.

• Collabora Office 26.04 Help: COSH — direct product-specific definition and syntax.
• Editorial testing standards.

The examples use semicolon argument separators. Displayed decimals are rounded expected values, not exact native outputs. Mathematical identities are explanatory calculations; product support is limited to the cited documentation scope.