COSH in SoftMaker PlanMaker 2026: hyperbolic cosine, syntax and examples

The mathematical definition is cosh(x) = (e^x + e^(-x))/2. COSH is even: COSH(-x)=COSH(x). Over the real numbers it has a minimum of 1 at x=0 and increases as |x| increases. This is not the ordinary cosine of an angle: =COS(0) is also 1, but ordinary COS(x) oscillates between −1 and 1, whereas real-number COSH(x) is at least 1. The official COSH page establishes PlanMaker’s function name and broad purpose; these additional comparisons follow from mathematics, not undocumented PlanMaker implementation.

Use COSH when a formula explicitly calls for the hyperbolic cosine: mathematical modelling, certain geometric curves, hyperbolic identities and comparison of symmetric positive/negative inputs. Do not use COSH for a conventional angle in degrees or radians unless your mathematical model specifically requires the hyperbolic function.

=COSH(Number)

The same one-argument function is documented in both the English PlanMaker 2026 and PlanMaker 2024 references. No multi-argument separator is needed for COSH. Examples use a decimal dot as shown in the English docs; whether a decimal comma, translated function name, numeric-text coercion or particular separators are accepted depends on locale/application settings and has not been natively checked. SoftMaker 2026 COSH · SoftMaker 2024 COSH, checked 2026-10-13.

Enter the inputs shown in A2:A8, place =COSH(A2) in B2, and fill downward through B8. The following are independently calculated expected values; increase displayed decimal places if comparing.

COSH(0.1) reproduces the rounded vendor example 1.005 at three decimal places. The long decimals above are expectations from Python’s math.cosh, not proven byte-for-byte values in a PlanMaker build. For financial and scientific calculations, inspect number formatting, rounding and data provenance rather than expecting every displayed digit to match.

1. A symmetric catenary-style curve (illustrative geometry)

The mathematical catenary form y = a*COSH(x/a) is a way to create a symmetric curve around x=0. This does not by itself calculate a real cable installation’s clearance, tension or safety factors; the correct parameter and physical model must come from engineering analysis.

Place 10 in B1 as the curve-scale parameter a, and 5 in A2 as a horizontal coordinate x. In B2 enter:

=$B$1*COSH(A2/$B$1)

The expected B2 result is approximately 11.276259652064 (in the same chosen length units as the two inputs). To calculate the mathematical height above its minimum at x=0, put in C2:

=$B$1*(COSH(A2/$B$1)-1)

The independently predicted C2 result is 1.276259652064. Change A2 to -5: B2 and C2 should remain unchanged because COSH is an even function. This simple two-cell model is valuable as a geometry demonstration, not a substitute for an engineered design.

2. Verify symmetry on an input table

With 1 in A2, put =COSH(A2)-COSH(-A2) in B2. The mathematical answer is 0. Repeat for several positive and negative inputs to identify sign mistakes in a longer model. At large magnitudes, number representation and runtime numeric limits may affect evaluation; this is a conceptual check, not a native PlanMaker precision certification.

3. Cross-check with exponentials

With 0.5 in A2, compare =COSH(A2) to =(EXP(A2)+EXP(-A2))/2. Both should give approximately 1.127625965206 by mathematical definition. The alternative expression is a validation identity, not a statement about internal PlanMaker algorithms. For very large positive or negative inputs, the EXP terms may overflow or cause numerical issues before a built-in function does; actual thresholds are not documented or tested here. SoftMaker EXP documentation · SoftMaker COSH.

4. Hyperbolic Pythagorean identity

With 0.45 in A2, enter =COSH(A2)^2-SINH(A2)^2 in B2. It should be 1, mathematically. A small floating-point discrepancy should be assessed using a tolerance such as =ABS(B2-1)<0.00000001, rather than strict equality. SINH is a separate, officially documented PlanMaker function. SoftMaker SINH.

5. A logarithm-based exact-value check

Place 2 in A2, and type =COSH(LN(A2)) in B2. The expected mathematical result is exactly 1.25, since cosh(ln 2) = (2 + 1/2)/2. Contrast =SINH(LN(A2)), which is expected to be 0.75. The input to LN must be positive. This is a reproducible relationship check rather than evidence that the two engines perform identically in all corner cases. PlanMaker LN.

The official function reference does not enumerate all error codes, numeric-text conversion rules, extreme-input thresholds or platform-specific runtime limitations. This guide therefore does not promise #NUM!, #VALUE! or a specific overflow sentinel for untested cases. Likewise, whether an installation accepts named arguments or complex-number inputs is not established here. See official PlanMaker 2026 COSH.

Documentation-level syntax agreement does not verify actual interoperation for a saved Excel or PlanMaker file. For an important workbook, test the target version and locale using representative data and record any differences. SoftMaker 2026 · SoftMaker 2024 · Microsoft Excel COSH, all checked 2026-10-13.

• SINH — hyperbolic sine: use with COSH in identities and transformations.
• TANH — hyperbolic tangent: equals SINH(x)/COSH(x) mathematically.
• ACOSH — inverse hyperbolic cosine: inverse branch for inputs at least 1; ACOSH(COSH(x)) mathematically gives ABS(x), not x for negative x.
• EXP — exponential: useful for teaching the exponential definition.
• COS — ordinary angle cosine: separate trigonometric function for radians.

Claim-level evidence ledger (checked 2026-10-13): SoftMaker 2026 COSH confirms the function name, syntax, meaning and example; SoftMaker 2024 COSH supports historical documentation continuity; Microsoft Excel COSH supports only the stated Excel comparison and its named versions. The catenary, symmetry, logarithm and identity results are independent mathematics verified with Python; no native PlanMaker or Excel execution, screenshots occurred.