Interact with this resource for a minute or two. Then answer the questions that follow.
Why does the [b][color=#9900ff]purple arrow[/color][/b] represent the value of the [b][color=#9900ff]tangent [/color][/b]of the angle? How do you know this?
If we kept going around the circle (past [math]\theta=\frac{\pi}{2}[/math]), what would the graph look like (on the right) to the right of the vertical line [math]x=\frac{\pi}{2}[/math]?
Why are there vertical asymptotes at [math]x=-\frac{\pi}{2}[/math] and [math]x=\frac{\pi}{2}[/math]? Are there other asymptotes for the function [math]y=\tan\left(x\right)[/math]? If so, how would you describe where they are?