SEC in Collabora Office: Calculate Secants from Degree or Radian Angles

• 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.

=SEC(number)

number is a radian angle. Use RADIANS when the source value is in degrees. Where cosine is nonzero, SEC(x) equals 1/COS(x).

The function returns a dimensionless ratio. It is different from ACOS, which returns a principal angle from a cosine value. Secant is a reciprocal operation; inverse cosine is an inverse-function operation.

Enter 0, 30, 45, 60, 120 in A2:A6. In B2 enter and fill down:

=SEC(RADIANS(A2))

At zero the cosine is one, so secant is also one. At 120 degrees cosine is negative, giving a negative reciprocal. A negative secant is a signed trigonometric ratio; it is not automatically a physical negative distance.

For ordinary valid real angles, the mathematical magnitude of secant is at least one. Inspect any contrary result for a mistaken formula, units or function choice before assuming it is a new geometric interpretation.

=SEC(PI()/4)
=1/COS(PI()/4)
=SEC(RADIANS(60))*COS(RADIANS(60))

Expected results, approximately: 1.414213562, 1.414213562 and 1. COS supplies the forward cosine used by the reciprocal check.

Keep the underlying calculated values. Retyping a rounded secant before multiplying by cosine can create a small discrepancy that reflects lost display precision rather than a different identity.

For a right triangle with adjacent side 9 units, let A2 contain an acute angle in degrees. Calculate:

=9*SEC(RADIANS(A2))

At 30, 45 and 60 degrees, expected hypotenuses are approximately 10.392304845, 12.727922061 and 18 units. All exceed the adjacent side, as this geometry requires.

An angle of zero would give the limiting value 9, but would not describe a nondegenerate triangle with a positive opposite side. Keep mathematical controls separate from the model’s allowed inputs. Angles outside the acute interval can give valid signed function values without representing the same ordinary right-triangle diagram.

The 60-degree case is a useful check because its secant is exactly two mathematically. If the result is not near 18, inspect whether A2 was degrees or radians and whether 9 was the adjacent side.

=SEC(RADIANS(-60))
=SEC(RADIANS(60))
=SEC(RADIANS(45))^2
=1+TAN(RADIANS(45))^2

Expected results: 2, 2, 2 and 2, within numerical precision. Secant is even, so opposite angles have the same value. The final pair checks SEC(x)^2 = 1+TAN(x)^2 at an allowed angle.

TAN is used here as part of the identity. Do not treat a coincidental equality in one table as evidence that SEC and TAN are interchangeable; their definitions and values differ generally.

Secant is mathematically undefined where cosine is zero: PI()/2 plus an integer multiple of PI() radians. Nearby values can be large. At 89 degrees, SEC is approximately 57.298688499; at 89.9 degrees, it is approximately 572.958086019.

For a worksheet quality check, expose =ABS(COS(RADIANS(A2))) in a helper column. A small denominator warns that input uncertainty can be strongly amplified. Any chosen rejection tolerance is a model-specific rule, not a universal SEC argument limit.

A nominal 90-degree formula can be stored as a floating-point approximation. Do not promise that every client displays the same error instead of a large finite result. The official section reviewed describes the reciprocal definition but not a complete extreme-input error matrix.

This guide has not run native Collabora singularity or extreme-angle tests. Its numerical examples use finite, ordinary inputs and explicitly avoid claiming that symbolic identities guarantee bitwise equality.

• Collabora Office 26.04: SEC.
• 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.