The Inverse Tangent

Look at the graph of the tangent:

You immediately see that we can easily just chop that one part. As you obviously can tell from the graph, as we take values of x that get ever so close to pi/2, we get an infinitely larger value, but not actually touching pi/2.
Similarly, as we take values of x that get infinitely closer to pi/2, the output of tan(x) gets infinitely smaller.

So, in terms of the inverse, as we take values that go infinitely big, we get infinitely close to pi/2.
Similarly, as we take values that go infinitely small, we get infinitely close to -pi/2.

This is the inverse tangent, denoted by arctan(x): You'll use pretty much the same line of thought to then learn about The Inverse Cotangent