In words, arctan(x) is the angle formed by a right triangle whose side opposite the angle and adjacent sides have ratio x/1. What is the measure of the other non-right angle in this hypothetical triangle, and what would the tangent of this other angle be?
what's the sum of the angles in a triangle? Trig functions assume that one angle is 90 degrees. If one angle is [itex]\theta[/itex], then what's the other? Draw a triangle to aid you in this. Make one such that [itex]arctan(v)=\theta[/itex]. What's the other angle? What's the tangent of this other angle?