Zoho Sheet SECH Function: Hyperbolic Secant Examples

Zoho’s official SECH reference was retrieved on October 15, 2026. This establishes documentation in the rolling web service, not the original introduction release or a final functioning-version endpoint; both historical endpoints remain unverified. Mobile/offline parity is not established. Additional numerical examples below were independently calculated. No native Zoho Sheet execution or cross-product import test was performed.

SECH(angle)

Zoho names the one required argument angle and describes it in radians. Its published examples use numeric values directly. The SECH entry also recommends a degree-to-radian conversion when the source is actually a degree angle. That wording is not a reason to convert an already dimensionless model input. For an equation written as sech(x/a), use x/a directly when x and a have the same unit. No optional arguments are documented.

Mathematically, sech(x) = 1/cosh(x). The official COSH entry documents the helper used below. This is hyperbolic mathematics, not the periodic circular function SEC. A single-argument call has no delimiter; use the spreadsheet’s local numeric punctuation.

Create SechControls. Put Input in A1 and Result in B1, enter the three numeric inputs below, and fill =SECH(A2) from B2 through B4.

These three pairs match the vendor’s rounded examples and were independently recalculated. They are documentation-backed expectations, not native observations. Keep full values in formulas and round only the displayed results.

Create SechComparison, reserving A1:D8. Put Input, Direct, Reciprocal and Difference in A1:D1. Enter the values below and fill the formulas through row 8:

B2: =SECH(A2)
C2: =1/COSH(A2)
D2: =B2-C2

D is mathematically zero. A tiny floating-point difference is possible because the formulas may take different computational paths. SECH is even: changing the sign of the input preserves the output. Its value is 1 at zero and lies between 0 and 1 for finite real inputs. These properties are mathematical checks, not a guarantee about every extreme floating-point input.

Duplicate the table and change only A6 from 0.5 to -0.5. B6/C6 become approximately 0.886818884. Other rows stay unchanged. The unchanged magnitude demonstrates even symmetry. A control that references the actual changed cell is more useful than repeating a literal-only formula.

Take the hypothetical equation output = 4*sech(x/a), with positive scale a = 2. This is a demonstration of that equation, not a physical-law claim. Create SechProfile with x, a, Ratio and Output in A1:D1. Enter A2:A5 = 1,2,4,6, B2:B5 = 2, then fill C2 =A2/B2 and D2 =4*SECH(C2) through row 5.

In a copy, multiply every A and B input by 100. Ratios and outputs stay the same because the conversion affects numerator and denominator equally. Changing only A changes the model. In another copy, replace the leading multiplier 4 with 8: every output doubles. These checks isolate unit conversion from amplitude changes.

A peak profile and its half-height

For the supplied model, the center at x = 0 has output 4. In H2 enter numeric 1.316957896924817, an independently calculated approximation to ln(2 + √3). In H3 enter =4*SECH(H2); the mathematical expected result is approximately 2. This is a model check, not a fitted width estimated from measurements. The profile is symmetric about zero.

Zero is mathematically safe for SECH because cosh(0)=1. At large magnitudes, the result approaches zero, but underflow thresholds and implementation details are not documented by these examples. A hand-written expression involving EXP can overflow internally even when the final mathematical value is small. Prefer the documented function and test the actual magnitude range your workbook needs.

Zoho states an input limit below 2^27 = 134,217,728, and associates larger values with #NUM!. Its wording does not settle equality at the boundary or whether the bound applies to the signed input or its magnitude. The examples here stay far inside either reading. Do not substitute an Excel absolute-value rule or infer behavior for huge negative inputs without a Zoho test.

The reference also identifies invalid-type/name/reference errors. Its generic glossary is not a complete specification of blank-cell coercion, numeric text, arrays or every numerical exception. Check a literal first, then the referenced cell, and retain the original input when diagnosing a failure. Exact runtime error displays have not been observed here.

COSH supplies the denominator, while SEC belongs to circular trigonometry. COTH is another hyperbolic reciprocal with its own domain. Cross-product names do not prove exact error, precision, coercion or platform equivalence; validate transferred workbooks in their actual application.