When you plot cotangent values on the Cartesian plane, as with tangent values, at certain points you cannot define them. As the discussion in Table 12.5 indicates, if the value of the sin θ is 0, then the value of the cotangent is undefined. When you plot cotangent values, the resulting curve rises indefinitely as it approaches a line extending vertically from any point on the x coordinate at which sin θ is 0.
A formal way to say this is that cot θ is not defined at any value of π + kπ. The value of k can be any integer. Given this situation, as Figure 12.19 illustrates, such values are 0, π, 2π, 3π, −π, −2π.