Cotangent Function

Let P be the point of intersection of the terminal side of an angle in standard position and the unit circle. The cotangent function, denoted by cot, is defined as the ratio of the x-coordinate to the y-coordinate of P.

Recall that the x- and y-coordinates of this point correspond to the cosine and sine of θ, respectively. Therefore, the cotangent function can also be defined as the ratio of cos θ to sin θ.

Since division by 0 is not defined, the graph of the parent cotangent function y=cot x has vertical asymptotes where sin x=0. This means that the graph has vertical asymptotes at every multiple of π. The graph of y=cot x can be drawn by making a table of values.

Consider now the general form of a cotangent function.

Here, a and b are non-zero real numbers and x is measured in radians. The properties of the cotangent function are stated below.