Now for the Tangent and Cotangent graphs, everything changes! Then all we have to do is graph “U’s”! Don’t worry, it will all make sense once you see it in action.

Oh, a vertical asymptote is a line that our function will approach but never touch or cross. Once we have the reciprocal curves sketched, all we have to do next is place vertical asymptotes anywhere the reciprocal graph crosses the center line. The awesome thing about these two graphs, is that all we really have to do is graph their reciprocal functions first (i.e., the sine or cosine curves), which we already know how do to! We will start with the Cosecant and the Secant graphs. Why would these four graphs have discontinuity, or breaks?Īll of these functions are built from sine and cosine, and they all have denominators! And because they all have denominators, that means we need to make sure we never divide by zero! Well, it is any place where there is a gap or a break in our graph, meaning we are indicating any place where our function is undefined, as nicely stated by Interactive Mathematics. What is most interesting about all four of these graphs is that we encounter discontinuity! In this lesson we are going to learn how to graph the other four trigonometric functions: tan, cot, sec, and csc.