I believe when we were first introduced to the radian, it was explicitly defined in terms of the radius, i.e. 1 radian = an angle whose arc length is equal to t

I believe when we were first introduced to the radian, it was explicitly defined in terms of the radius, i.e. 1 radian = an angle whose arc length is equal to the radius of the circle. Was a radian just defined as an angle of 57.3 degrees in your class? I imagine that would seem really arbitrary to students.