Fourier Series and Mandelbrot Set in trig?

I joined just for this ridiculous question. A friend of mine has asked of my help. She's in a Trig class at a community college, and I tutor at one myself. Having taken everything through Calc 3 and Differential Equations, I seemed like the guy to ask.

Well, her teacher has asked her to explain, create examples, and solve both **Fourier Series** and the **Mandelbrot Set** in her basic trig class. Apparently he's a calculus teacher primarily, and really doesn't pay attention to the actual coursework. It was assigned Friday afternoon to be turned in before the Monday morning final, of which they will be covered on the test. No examples given, nothing. It rather enrages me.

I cannot find anything online explaining either of these without calculus (and they're tough even for me), so given it's a trig forum, I'm appealing for help here. Is there a way of explaining these concepts to her without need of calculus?

Thanks in advance for looking it over, even if you can't help.