In this lesson we are going to learn how to graph the other four trigonometric functions: tan, cot, sec, and csc.
What is most interesting about all four of these graphs is that we encounter discontinuity!
Discontinuity? What’s that?
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.
Why would these four graphs have discontinuity, or breaks?
All 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!
Oh, ok that makes sense. So how do we graph them?
We will start with the Cosecant and the Secant graphs.
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!
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.
Oh, a vertical asymptote is a line that our function will approach but never touch or cross. It’s behaves like boundary lines.
Then all we have to do is graph “U’s”! Don’t worry, it will all make sense once you see it in action.
Graph of the Tangent Function
Now for the Tangent and Cotangent graphs, everything changes!
What we first discover is that for these functions our period is no longer a complete rotation around the unit circle, but rather it is cut in half!
So with a dramatic change in our wavelength, we will also see that these functions like to dance!
You read that correctly… tangent and cotangent look like the classic dance from the movie Saturday Night Fever.
Don’t worry if you’ve never seen the film, these two cool functions can also be compared to our Cubic function from Algebra 2.
Together, will learn the steps for graphing the Tangent and Cotangent, with all of their tricks and twists and see how they are similar and different from our basic Sine and Cosine curves.
- Secant & Cosecant Graphs: Learn how to graph both sec and csc trigonometric functions. This handout includes 4 worked out examples.
- Tangent & Cotangent Graphs: Learn how to graph tan and cot trig functions. This cheat sheet includes both the formulas and 4 detailed examples.
Graphing Reciprocal Trig Functions – Video
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