Zoho Sheet SEC Function: Secant and Sloping-Length Examples

Zoho’s official SEC 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.

SEC(angle)

The single required numeric angle is in radians; no optional argument is documented. For degrees, the official entry gives multiplication by PI()/180. RADIANS performs that same unit conversion. Apply it to the input, not to the finished secant result.

SEC is not an inverse cosine. ACOS finds an angle; SEC calculates 1/cos(angle). SECH is hyperbolic secant and has a different contract. A one-argument SEC formula has no separator; decimal punctuation should follow the spreadsheet’s locale.

Create SecControls. Put radians in A1 and result in B1; enter 0.3, -0.9, 30 in A2:A4. Enter =SEC(A2) in B2 and fill through B4. The published results are 1.046751602, 1.608725810, 6.482921235, respectively, with a trailing zero added to the middle display for nine decimals.

The third input is thirty radians. It is not an example of thirty degrees. In D2 enter =SEC(RADIANS(30)): its mathematical result is approximately 1.154700538. Keeping both controls visible makes the unit difference explicit.

Create SecDegrees, with Degrees, Secant, Reciprocal_cosine and Difference in A1:D1. Enter the degrees below in A2:A8. Fill these formulas through row 8:

B2: =SEC(RADIANS(A2))
C2: =1/COS(RADIANS(A2))
D2: =B2-C2

D is mathematically zero; allow a small numerical tolerance rather than demanding identical internal floating-point results. Secant is even, so ±30° have the same value. At 120°, the negative value follows the cosine sign and is unsuitable as a physical triangle length without a different geometric interpretation.

Duplicate the sheet as ChangedSecAngle and replace only A5, originally 60, with 30. B5/C5 change from 2 to approximately 1.154700538; other rows remain unchanged. The control exposes formulas that accidentally reference the wrong row.

Create SlopeLength with Horizontal_run, Angle_degrees and Length in A1:C1. Enter 10 in A2:A4 and 20,30,40 in B2:B4. Fill C2 =A2*SEC(RADIANS(B2)) through C4. Expected lengths are 10.641777725, 11.547005384, 13.054072893 in the same unit as the horizontal run.

This assumes a straight segment and an acute angle above horizontal. In a copy, double all runs to 20: every length doubles. In another copy, preserve the run but change only the 30° angle to 60°: that row becomes 20, demonstrating that angle changes are not a simple unit rescaling.

A length entered along the slope is already the hypotenuse. Multiplying that length by SEC again would answer a different question. Label measurement columns explicitly and retain the original inputs.

Secant has no finite mathematical value where cosine is zero, including 90° and 270°. A stored approximation to π/2 need not have an exactly zero cosine, so a formula near a pole may return a huge finite number. This guide does not promise a specific zero-denominator error token for Zoho.

Results can be highly sensitive to small angle changes near those points. The sample table avoids poles. A cell displayed as 90° may contain a nearby value rounded for display; inspect the underlying number before interpreting the result.

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.

Cosine supplies the reciprocal check, RADIANS converts degrees, and ACOS solves the inverse-angle problem. SECH is a distinct hyperbolic operation. Shared names in other products do not establish matching precision, errors or version support; test the small controls in the destination app.