Using the definition of the arctangent function, what are the domain and range of the arctangent function?

Determine the following values exactly: \(\arctan(-\sqrt{3})\text{,}\) \(\arctan(-1)\text{,}\) \(\arctan(0)\text{,}\) and \(\arctan(\frac{1}{\sqrt{3}})\text{.}\)

A plot of the restricted tangent function on the interval \((-\frac{\pi}{2},\frac{\pi}{2})\) is provided in the following figure. Sketch its corresponding inverse function, the arctangent function, on the same axes. Label at least three points on each curve so that each point on the tangent graph corresponds to a point on the arctangent graph. In addition, sketch the line \(y = t\) to demonstrate how the graphs are reflections of one another across this line.

Complete the following sentence: “as \(t\) increases without bound, \(\arctan(t)\) \(\ldots\)”.