I was trying out Dimensional Analysis on a few equations and realized that angles have no dimension. Otherwise equations such as $s=r\theta$ are not dimensionally consistent.
Further, why don't trigonometric ratios have any dimension?
PS: I couldn't find any appropriate tag for this question. Could someone re tag as appropriate? Thanks.
Compare to a ratio of weights, it is weights that you compare. You get no units for the ratio, right ? I mean the result is independent of choice of units. But with angles your ratio is with lengths ! not angles ! so don't be surprized that you get "units". Any partition of an angle is named with "units" The funny thing is that unit transformation with angles obeys the same laws as with any other unit.