I want to know why 3 types of trig graphs have the shape that they do:
Secant graphs. Why would $\dfrac {1}{\cos \theta}$ result in a graph like this? I get the cosine graph - it makes sense when you compare it to a unit circle. But I don't understand it at the same level for secant graphs. Can someone please explain why the secant graph is shaped like that given it's equation?
Cosecant graphs. Same as above.
Cotangent graphs. Why would $\dfrac {1}{\tan \theta}$ cause the tangent graph to flip? Because when you look at a cotangent graph, it's basically a reflected tangent graph. Why would $\dfrac {1}{\cos \theta}$ create a graph that looks like that?
Can you please give the explanation for why the graphs are shaped like that not too rigorously, and at the level of a Precalculus student who hasn't learnt Calculus yet? Thank you.
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