The Tangent and Cotangent

The tangent function, introduced in the beginning as the ratio of the opposite over the adjacent vertices of the angle, equivalently, the ratio of the sine over the cosine is defined and denoted as Notice what happens to cos(x) from its graph, as we go to pi/2 (90 degrees):

It approaches zero. We have a zero in the denominator. In reality, it can never be zero, so the tangent will not exist for pi/2 or -pi/2.

The closer you get to zero in the denominator, the larger the result grows, to an infinitely larger value.

Indeed, the graph of tan(x) is the following:

Now, we'll talk about something called The Cotangent:
The cotangent is simply the reciprocal of The Tangent.

It's defined as Now, let's substitute a bit, we know tan(x) to be the ratio of sin(x) over cos(x):As you know, and if you don't, you're about to learn an useful trick, dividing by a fraction is the same as flipping that fraction over then multiplying instead of dividing.
Concluding: Take a look at the graph of the sine now. The sine is zero for zero. As we approach zeroes, we once again get infinitely large or small numbers. The graph of cotan(x) is:

A few extra functions will then be briefly defined:
The Secant and Cosecant