ACOS in Collabora Office: Find Principal Angles from Cosine Ratios

• Introduced: documented in Collabora Office 26.04 Help; the original introduction version is not established by the reviewed history.
• Availability: the official ACOS 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.

=ACOS(number)

The input is a cosine ratio. For a real result it must lie between −1 and 1 inclusive. It is not an angle to be converted directly, and a percentage-looking display should be checked against its underlying value.

The official help defines the principal interval 0 to π and recommends DEGREES for degree output. The real-input domain follows from the cosine range. Exact application-specific error codes for invalid inputs are not claimed here.

Enter 1, 0.5, 0, −0.5, −1 in A2:A6. In B2 enter and fill down:

=DEGREES(ACOS(A2))

Expected outputs: approximately 0, 60, 90, 120, 180 degrees. Negative cosine ratios produce angles in the second half of this principal interval.

In radians, =ACOS(0) is approximately 1.570796327, and =ACOS(-1) is approximately 3.141592654. The numbers differ from their degree representations because the unit differs, not because a different angle was calculated.

For a mathematical right triangle with adjacent side 3 and hypotenuse 5:

=DEGREES(ACOS(3/5))

Expected result: approximately 53.130102354 degrees. The ratio is 0.6. Use the same length unit for both sides before dividing.

For the complementary angle based on opposite side 3 and hypotenuse 5, ASIN gives approximately 36.869897646 degrees. The two angles sum to 90 degrees in this right-triangle example, but ASIN and ACOS are not interchangeable functions.

=DEGREES(ACOS(COS(RADIANS(-60))))

Expected result: approximately +60 degrees. Cosine has the same value at +60 and −60 degrees, and ACOS chooses the nonnegative principal angle.

If the task requires clockwise versus counterclockwise direction, a single cosine ratio is insufficient. ATAN2 uses both signed coordinates and can retain the quadrant information that this composition loses.

Take vectors (3,4) and (4,3). Each has magnitude 5, and their dot product is 3×4 + 4×3 = 24. The cosine of their angle is therefore 24/25 = 0.96:

=DEGREES(ACOS((3*4+4*3)/(SQRT(3^2+4^2)*SQRT(4^2+3^2))))

Expected result: approximately 16.260204708 degrees. This is the unsigned smaller angle between these nonzero vectors in the ordinary Euclidean model.

A zero vector has no direction and makes the denominator zero. Validate magnitudes before dividing. The formula does not supply uncertainty bounds or make an engineering decision about whether an angle is acceptable.

For a numeric ratio in D2:

=IF(AND(D2>=-1;D2<=1);DEGREES(ACOS(D2));"Review ratio")

With 0.6, 1.05 and −1.05, expected results are approximately 53.130102354, Review ratio and Review ratio. Keep the raw value and its source calculation available for review.

Floating-point calculations can sometimes produce a tiny excursion outside a theoretically valid bound. Any tolerance or clipping policy should be justified by that calculation’s error scale. Clipping a genuinely invalid measurement to the boundary silently changes the data.

Results near ratios ±1 are sensitive to small input changes. Do not round the ratio prematurely just to make a displayed angle look simple. Preserve calculation precision and round only the final presentation when appropriate.

=COS(ACOS(0.6)) is expected to return approximately 0.6, providing a simple inverse-direction check inside the domain. It does not prove that the original ratio represented a valid triangle or vector measurement.

Use COS for angle-to-ratio conversion and DEGREES to label the output unit explicitly. Check a known endpoint and an interior value before adopting the formula in a larger workbook.

• Collabora Office 26.04 Help: ACOS — 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.