Graphing trigonometric functions

Okay, so my book spends a whole lot of paper and ink talking about these, but it never goes and explicitly breaks down what's going on.

What would help my understanding immensely is if someone took the following functions and broke down what each variable did on the graph.

and the equivelents for the secant and cosecant functions. (cos and cot behave the same way as sin and tangent if I'm getting anything at all from the book) I'm having a lot of trouble because my book and the online video lectures split the sections up differently and emphasize different parts.