By means of Math, the harmonic functions (sin and cosine) are defined for Arcs, not for Angles, as arguments. Naturally, angles expressed in Degrees and arcs expressed in Radians are proportional. That's why it makes sense to use Angles as arguments for harmonic functions in calculators and tables (i guess you've never seen a trig table).
In the Physics (including Engineering), when you treat any oscilation, such as Harmonic Movement or Eletromagnetic Wave, you're allways dealing with something like 2*pi*f*t, where f is frequency and t is time. When they're multiplied they become adimensional, remaining only Radians as the unit of 2*pi arc.
When you do so, the 2*pi arc (in radians) and f (in Hz) are tighten together in a angular frequency expressed in Radians per Second. Converting this frequency into Degrees per Second may turn your Math sentence incoherent if there's any other term reffering to frequency in any part of your system. That's why such transformation (eg Laplace) virtually never happens in Degrees in any calculator.
I'm not sure I have been clear. Please ask me if you'd like to have more info.