/sci/ - Science & Math

Hi anons, i'm taking a precalc class and I was wondering if someone here could provide me some insight. Most of the class is just trig and the unit circle. I know how to solve the problems fine enough, but unlike Algebra 1-2, I wouldn't say I have gained any deeper understanding or insights of the subjects. How do you gain an intuitive understanding of mathematical principles? At what point in your education would you say you began to "get" things. I have occasional "aha" moments but I feel like largely i'm jut memorizing the identities and the rules to get a solution arbitrarily, with only a fuzzy and vague understanding of why I make each step.
The usual answer I receive is to go over an intro to proofs book, but the one's i've seen all say you should have familiarity and experience with up to "Calculus I" first, and i've never taken a Calculus course before.
Here's the textbook we use for the course If anyone has interest I can probably upload a PDF, i'd appreciate if someone can tell me whether it look quality or not, and also if anyone has any textbooks they do recommend.