Reading Trigonometry material from AoPS

[Gil]

My kid wants to know:

If he does the Trig chapter from Intro to Geometry then can he do the Trig chapters from the Precalculus text, or is there material in the AoPS Algebra books that also covers trigonometry?

or Can he just start the Trig related chapters from Precalculus, without reading anything from Intro to Geometry first?

He's read the Table of Contents for Intermediate Algebra and was wondering if some of the lessons touch on or expounded upon the Trig material introduced in Intro to Geo?

[kiana]

I personally prefer starting with right triangles, so I would do the geometry chapter first. But this is a subject of debate, not one where people tend to agree. 

He won't need to do the intermediate algebra text -- the algebra prereq for trig is more to really understand functions. My trig students tend to not really "get" the difference between f(1/2) and f(x) = 1/2, and even if they will write it carefully, it's just to humor their meanypants teacher. I doubt this will be an issue. 

[kiana]

I've found that when I start with the unit circle, they seem to forget about triangles and forget that it's supposed to actually mean something in a physical context. They just look at it as a magical black box (which they're prone to anyway). 

It also lets me throw in the word problems sooner, and give problems designed to set up for the inverse trig triangles later on, e.g. draw three triangles where cos theta = 2/3. I can do this with the x/r definition as well, of course, but it doesn't seem to click as well. I think some weakness in analytic geometry is going on here as well. 

I also like the derivation of the 30-45-60 values better, and giving the triangles as a mnemonic works for me. 

[kiana]

Understanding that the point (2, 1) means that the distance from the x-axis is 1 and the distance from the y-axis is 2. I mean really understanding, beyond a formulaic "count two right and one up". Understanding that the distance formula IS the pythagorean theorem. 

When I transition to the unit circle (which is after only one chapter), we still draw triangles inside it for some time, and that seems to help with that. 

I forgot to mention that allowing me to use non-fractional values for sidelengths is another reason.