In engineering text books, sure they use radians. In mechanical engineering design if you put a radian on a geometrical dimensioning and tolerance sheet it's not going to go well for you.
I suspect the same holds for civil engineering too. I have my doubts that radians are useful in chemical engineering, but I could be wrong there.
Fair, I was mostly thinking electrical engineering and similar. For civil engineering, I'm curious what is common. As soon as you have Fourier and/or Laplace Transforms, you will most likely end up using radians, and are these not relevant for civil engineering? I have no idea, though the modeling of linear, time-invariant systems (i.e. filters) strike me as important if you're building, say, a bridge, and/or care about seismic activity at all.
Nevertheless, in the context in which this was presented, radians are the only way to go.
Output on control system HMI Scada screens for stuff like Tilt Drives are all in degrees as well, in this respect it's like the Kelvin scale. Control system doesn't display thermocouple readings in Kelvin either (at plant I work at Temperature setpoints are displayed as degree Celsius).
You might use Radians/Kelvin internally for ease of calculation but they aren't numbers you quote around or report things in.
I would be very surprised though if the people who actually implement the control systems (as in doing the hard math) don't use radians, though. Is that really not the case? Using degrees just seems like unnecessary extra steps when dealing with transfer functions...
Internally yes they probably convert but it is not exposed anywhere, kind of like Chemical reaction you convert everything to Mols internally to do the calculations but externally you report all of the inputs as a mass.
The control system won't tell the operator to add an extra 0.3 mols of reactant or to tilt the furnace by Pi/4 radians
I suspect the same holds for civil engineering too. I have my doubts that radians are useful in chemical engineering, but I could be wrong there.