Hello, I am taking a refresher trigonometry course in college using Lial and Hornsby's Precalculus which introduces some topics I'd never encountered before, like parametric equations and different kinds of polar graphs like lemniscates, cardioids, etc. These topics seem fascinating but the book gives only a cursory overview of them. In addition it gives tantalizing mention of other things like orthogonal vectors, the Julia set, eccentricity of conic equations, trochoids, Bezier curves, Lissajou figures, and many different applications. What are these kinds of topics called, and are they covered in calculus?

I would really like to find a good book to study them, and to get a better understanding of more basic topics, because as it is I feel like I can pass tests but I don't really understand what it is I'm doing. I hate the textbook we're using because it is not very rigorous and tries to cover too many topics without developing them (instead there are just a lot of pictures and "online resources"). I have done really well with the Saxon books in the past and from looking at them I really like the way the Undergraduate Texts in Mathematics tend to be structured. Does anybody have any recommendations for books covering trigonometry and these more advanced topics which don't assume too much knowledge but also don't treat you like you have ADD? I never learned trigonometry properly in high school and so far this class hasn't done a lot to increase my feel for it. I'm not a math major but I would really like to understand it better.