Graphing Trigonometric Functions and computing their derivative

For an upcoming midterm, I need to be able to do the following: graph, indicate direction & speed, compute the derivative, and find critical points of trigonometric and hyperbolic functions.

For example:

What perplexes me is the form: (a, x) with respect to theta. Are these parametric plots or the two functions mapped onto one plot? My interpretation is that they are parametric. So, for example,

Should be a unit circle except and

If this is true, do I take the derivative of and ?

But then the plot of its derivative is also graphically the same as the original function. Any help would be greatly appreciated, thanks for your time.