Reviewing what we learned earlier in this unit, we know that asymptotes appear wherever there is an undefined value. Furthermore, we learned that undefined answers are produced whenever we attempt to divide by zero.

In the Unit Circle, the ratio for tangent is "y/x" and the ratio for cotangent is "x/y". Where the denominator of "x" equals zero (pi/2 and 3pi/2) determines where the asymptotes for tangent are located. The same applies to where the value of "y" is equal to zero in a cotangent graph (0pi, pi, 2pi).