why is it an invalid argument to find the inverse tangent of 22 divided by 11
You can certainly find tan-12 so I don't know what you mean.
Is this a part of a bigger question?
atan(22/11) = atan (2) = 63.434948822922º
Mmmmm.....looks perfectly valid, IMHO......(We're just asking ourselves, where does the tangent = 2 ??......Note that it has to be greater than 45º but < 90°)