I have been teaching trigonometry for many years and, surprisingly, did not know of this issue. I read the responses and the references therein, and I am putting my thoughts on this issue here.
The question is how to approach trigonometry, right triangles first and then unit circle; or circle first and then triangle.
I think the answer depends on the ...
Chris. I know you are really excited about this idea, but I'm very worried about a critical omission from your list of considerations.
I notice that you teach at a college with a lot of faculty members. One of the biggest blind spots that many faculty (and apparently, you) have is which publisher resources their fellow faculty use.
Some use online ...
Books about middle school algebra and trigonometry written by someone like Gelfand are rare (I don't know other examples; for example V.I. Arnold's books nomially for children are aimed at very special children, their author's claims to the contrary), but there are many undergraduate textbooks written by superb mathematicians. I list below some that occur to ...
This may not qualify, as it is a stretch to classify this as a "textbook."
It arose from a series of lecture Klein gave to high-school teachers.
Klein, Felix. Elementary Mathematics from an Advanced Standpoint: Geometry. Transl. from the Third German Ed. by ER Hedrick and CA Noble. Dover, 1939.
I love this (...
I wonder if one could run a geometry course through GeoGebra? This requires laptops or workstations, but the software is free.
I am not finding the ideal textbook based on GeoGebra, but here are two links
that give some sense of what is available.
GeoGebra Geometry App: Beginner Tutorials with Lesson