Why is lat/long "backwards?"

[MAKG1]

I had tried that formula for bearing at least 3 times in the past and always got an error. For some reason it finally works.

I find it much easier to do the spherical trig with rigid body rotations in Cartesian coordinates. Those naturally make great circles, and aren't too hard to encode and decode.

It's faster as well (by quite a lot), especially when you start using quaternions.

It's pretty easy to mistype something, for instance using degrees instead of radians or mixing up latitude and colatitude. Or just misplacing a parenthesis.

There are a few conventions you can use to keep it straight, and it's important to write them down, whatever you might choose. Like, longitude is east-positive, heading is north through east (careful! that's left handed), all angles are in radians (important), and so on.

It's even worse in astronomy, since the "longitude" conventionally has units of hours, but the "latitude" is still in degrees. What's a factor of 15 between friends?