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Best Answer: You're wrong about what the arctan function is. arctan is that function that answers the question, What angle theta yields the tan (theta) = x? arctan 0 = 0 because the tan 0 = sin 0 / cos 0 = 0/1 = 0.
As Quora User said: It is the ratio of the length of the arc to the radius which defines the angle subtending the arc.So if the arclength and radius are each measured in miles (or any other common unit), the units cancel, leaving radians as a unitless measure.