I have been using atn(1/6) for our standard tapered ball joint angles in 3D CAD. All derivations and definitions of the function say it should give me the angle. It's close, but when I force a 1:6 ratio angle it results in an angle of 9.527283˚. atn(1/6) yields 9.462322˚ Can anyone explain why there is a difference? Using a calculator yields the same thing as function in CAD. The difference is enough for our tapers not to seat correctly. The black dimensions are driving dimensions and the grey dimensions are resultants. The "Σ" indicates where the atn() function is being used. arctan should give me the same angle as a 1:6 triangle. (shown below)

**Forced 1:6 ratio to find actual angle**

**Used arctan(1/6) to find side length**