You will find textbooks for all of these at artofproblemsolving.com. They formed in order to help students like you.
I have used their number theory book, while tutoring a young student (who was great at math), and I loved it.
It all depends on the background (i.e. the axiomatic assumtions your students are able to cope with).
I recevied, in 1973, my trigonomtry in the same order, but at the time I was already quite familar with the right triangle geomerty.
My father, who studied trigonometry for surveing purpose, not mathematics, did recived it after an introduction to ...
I disagree with the notion that the unit circle approach preceding the triangle approach should be, if it is contextualized historically, "baffling." To this end, I suggest two pieces if you are wondering about how the unit circle gets itself into the pedagogical broaching of a subject that etymologically appears to be the study of triangles/three sided ...
There are no Amazon reviews. Doesn't seem like a popular title. (Just an indicator, not a Euclidean proof...but a negative note.)
The preface says that it is approaching teaching all of graph theory via this one graph as motivation. Seems rather non-standard. Again, not Euclidean proof, but a negative indicator.
If you are self studying AND a weak ...
I find it easier to think about a single number (x or y of unit circle) than a ratio.
Also helpful with angles greater than 180 or negative.
I learned it this way back in the early 80s...so it's not like some totally new fangled approach.
Just because it seems strange to you or you get some agreement on this message board, doesn't validate your opinion....
I've noticed this trend as well, and it's baffling.
The only justification I can see for it is that one of the main topics in precalculus is "functions," so they introduce the sine and cosine functions first. Then they say "Hey, guess what, these apply to triangles."
However, this strikes me as being completely backward: they should introduce the sine ...
Assuming you are teaching at the undergraduate level,
here are two free books you might explore to help clarify your question:
(1) Paul E. Pfeiffer, Applied Probability,
Open Textbook Library.
"In addition to an introduction to the essential features of basic probability in terms of a precise mathematical model, the work describes and employs user ...