Cosecant Function

Let P be the point of intersection of the terminal side of an angle in standard position and the unit circle. The cosecant function, denoted as csc, is defined as the reciprocal of the y-coordinate of P.

Recall that the y-coordinate of this point corresponds to the sine of θ. Therefore, the cosecant function can also be defined as the reciprocal of sin θ.

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

Consider the general form of a cosecant function.

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