ACOS in WPS Spreadsheet: Recover Angles from Cosine Ratios

• Introduced: documented by 2019-05-30 in the official WPS lesson; original introduction is not established.
• Availability: WPS Office for Windows Personal; no numeric release is stated in the edition metadata.
• Scope: exact current supported builds remain unverified. The Windows lesson does not establish equivalent availability in other WPS clients.
• Checked: October 14, 2026 against function-specific documentation. Examples were independently calculated; no native WPS test was performed.

=ACOS(number)

The WPS lesson requires an input from −1 through 1 and states that the result lies between 0 and pi radians. Convert that output to degrees with 180/PI() or DEGREES.

The argument is a cosine ratio. Applying RADIANS to the ratio before ACOS would change the quantity rather than perform a needed angle conversion. Exact native out-of-domain error codes are not established by this selected source.

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

=ACOS(A2)*180/PI()

Expected degree results are 0, 60, 90, 120 and 180. Negative cosine ratios produce obtuse principal angles in this table; the output is not a negative angle.

Without conversion, zero cosine gives pi/2, approximately 1.570796327 radians. Keep that unit visible when comparing a spreadsheet answer with a degree-based drawing.

For adjacent side 4 and hypotenuse 5:

=ACOS(4/5)*180/PI()

Expected angle: approximately 36.869897646 degrees. This is the same acute angle whose sine is 3/5 in a 3-4-5 triangle.

The ratio must use the adjacent side divided by the hypotenuse for this interpretation. Interchanging those lengths gives 1.25, outside the documented real input range.

In a mathematical triangle with two sides 5 and 7 enclosing an angle opposite a side of 8, the cosine rule gives:

=ACOS((5^2+7^2-8^2)/(2*5*7))*180/PI()

The ratio is 10/70=1/7. Expected angle: approximately 81.786789298 degrees. The squared side opposite the desired angle is the term subtracted in the numerator.

The three positive lengths satisfy the triangle inequalities. ACOS does not independently validate all the geometry that produced a ratio; check those conditions before treating the number as a physically meaningful angle.

Take vectors (3,4) and (4,3). Their dot product is 24 and each length is five, so the normalized cosine is 24/25:

=ACOS((3*4+4*3)/(SQRT(3^2+4^2)*SQRT(4^2+3^2)))*180/PI()

Expected angle: approximately 16.260204708 degrees. Both vectors must be nonzero for the normalization. A zero vector would make the denominator zero before ACOS receives a meaningful ratio.

Using the unnormalized dot product 24 directly is not a valid substitute; it lies outside −1 through 1. Keep numerator and lengths in helper cells when auditing a longer vector calculation.

Cosine at 60 and −60 degrees is 0.5. ACOS returns 60 degrees for either shared ratio, so ACOS(COS(angle)) does not recover an arbitrary signed angle.

The ratio reconstruction =COS(ACOS(0.8)) instead has mathematical expectation 0.8. That direction begins with a valid ratio and is consistent with the documented principal branch.

A normalized ratio slightly above one can arise from an invalid model or numerical rounding. Do not silently clip arbitrary values; retain the raw calculation and use any tolerance only under an explicitly justified policy.

The direct WPS lesson supports real inputs, the zero-to-pi branch and degree conversion. Native last digits, very unusual imported types and exact current error behavior remain unverified. See COS for the forward function and SQRT for the length calculations.

• WPS Academy: ACOS lesson, 2019-05-30 (Chinese; Windows Personal scope).
• Editorial testing standards.

The direct WPS product lesson supports the stated function scope. Worked outputs are independent expectations, not captured native results or proof of support across all current WPS clients.