In This Chapter
Using sine and cosine to graph their reciprocals
Drawing the inverse functions on a graph
The functions cosecant and secant have similarities to one another not only because they're the reciprocals of sine and cosine, but also because their graphs look very much alike. As you see in this chapter, the easiest way to sketch the graphs of these two functions is to relate them to the graphs of their reciprocals. Doing so helps determine the asymptotes (where the curve approaches infinity or negative infinity), turning points, and general shape of the curves.
The cosecant function is the reciprocal of the sine function (meaning, the cosecant equals 1 divided by the sine). Even though the sine function has a domain that includes every possible number, that characteristic can't be true of its reciprocal. Whenever the sine function is equal to 0, the cosecant function doesn't exist. That fact helps determine the asymptotes you use to graph the cosecant function.
The domain of the cosecant function is any number except multiples of π, because those measures are where the sine function is equal to 0. You can use this situation to identify the asymptotes by simply writing ...