Correct, and that's in line with what I'm saying: The law of cosines isn't involved in the conversion from 3D to 2D in all projections--it's inadequate to the task. Further in the FAQ it talks about the Haversine formula which suffers when the points are extremely far apart, rather than being close to the poles. All spherical to planar mappings suffer in one way or other. Without knowing what type of map the OP is using, we can't be certain in exactly which ways it will suck. 8^)
Even when the law of cosines is used, the Z-axis isn't always the the same as either the geographic N/S axis or the magnetic N/S axis. It all depends on the feature(s) the map is trying to portray.
...yet another pedantic weenie
When your only tool is a hammer, all problems look like your thumb.