The Soviets sucked at a lot of things but their physics and math education was world-class. Gelfand has a series of textbooks on basic math (algebra, trig, analytic geometry) that are great too: https://www.amazon.com/Trigonometry-I-M-Gelfand/dp/0817639144/ref=mp_s_a_1_1?dchild=1&qid=1595963298&refinements=p_27%3AI.+M.+Gelfand&s=books&sr=1-1
I started my college math career with a lot of holes, including in trig, that I had to patch up. I had a great time working through the book Trigonometry by Gelfand and Saul. It prepared me really well for further work.
I can't recommend this textbook enough. I made it through high school trig not understanding a thing. When I got to college I worked through this book and suddenly everything makes sense.
Gelfand really knew how to teach math. His approach is to put a huge amount of the learning into exercises for the student. When you finish, you don't just "know" trigonometry. You understand it.
It also starts from the beginning. You don't need to know anything more than basic algebra. It will help if she has some familiarity with the Pythagorean Theorem too, but that's really the only thing.
Gelfand's Trigonometry
Gelfand, with a few colleagues, put together a series of high-school level books that are quite good. The ones relevent to pre-calc are probably
Thank you for helping out! These are some books I just ordered:
Any other suggestions will be welcomed :D
Gelfand's Trigonometry Book is really, really great. I'd recommend it to anybody.
I was in a similar situation to you a couple years ago. I did poorly in high school math but then went on to do college level math and was left with several holes including geometry and trig. Trig is pretty darn necessary. You could get by without learning much Euclidean geometry as long as you have a few important results like the Pythagorean Theorem and a basic intuition of geometry.
The good news is, a lot of high school classes teach these subjects pretty poorly. You have the opportunity to learn them right.
I learned trigonometry last year from this book by Gelfand. It's the best introduction to the subject I've found and I came out of it with a really great understanding of the subject.
If you know something about set theory and proofs, you probably have enough mathematical maturity to work with axioms and prove things from foundations, so if you want to learn some geometry, I'd suggest just picking up a copy of Euclid as well as possibly working with this book by Hartshorne.