Plotting Cosecant Values
The value of the cosecant is undefined when it falls on a vertical line passing through a point on the x axis at which the sine value is 0. The sine and cosecant functions are reciprocals of each other.
To plot a cosecant value, you can begin on the x axis at 
. The value of the cosecant at this point is 1. As you move to the left, toward 0 from 
, the value of the secant rises infinitely as it approaches 0. It is undefined at 0. Moving in a positive direction along the x axis from 
, the value of the cosecant increases. As they approach π, they become infinitely large. At π the value for the secant is not defined. After passing beyond π, the cosecant values, shift to below the x axis. They begin at an infinitely large negative value, and then increase as they move toward 
. At 
the value of the cosecant is −1.
The cosecant values create a periodic pattern that alternates above and below the x axis, and the period of the secant graph is 2π. As Figure 12.21 illustrates, a period begins at 0 and extends to 2π.
