Monday, 5 August 2013

algebra precalculus - On The Shape Of Trig Graphs To A Precalc Student

I want to know why 3 types of trig graphs have the shape that they do:




  1. Secant graphs. Why would 1cosθ 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?



  2. Cosecant graphs. Same as above.


  3. Cotangent graphs. Why would 1tanθ cause the tangent graph to flip? Because when you look at a cotangent graph, it's basically a reflected tangent graph. Why would 1cosθ 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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