I don't think of it as units (as the sibling comment pointed out, angles are dimensionless); I think of ° as a postfix unary operator that does the conversion.

I don't think of it as units (as the sibling comment pointed out, angles are dimensionless); I think of ° as a postfix unary operator that does the conversion. In other words, I read sin(x°) as a shorthand for sin(x*Pi/180).