That helps quite a lot, although for several, it's more programming-by-name than programming-by-semantics.

I'd like to be able to say the end angle has to be less than the start angle, that the unit has to be radians (AKA unit-less :), the unit of radius & that negative values are sensical, and so forth; and have all these properties checked by a compiler.

Which I can do in some modern languages, surprisingly. :)

Assuming you're right about the guesses for those parameters, we could go a little further. Let's define

   data Directionality = Clockwise | Anticlockwise

   data AngularInterval = {
     beginAngle :: Double,
     endAngle :: Double,
     directionality :: Directionality
   }

... and then we're down to three parameters, all of different types (so no opportunity for mistakes, assuming static checking) and who knows, you might even have other uses for AngularInterval.