[dhosek]

There’s a whole pile of math like this that kind of lies in this nether land between more advanced than you’ll get in most high school math¹ but less advanced than you’ll get in most college high school math that I was only ever exposed to when I took the classes for my teaching credential. One of my favorite was how cos/sin, tan/cot and sec/csc all can be derived from right triangles on a unit circle with the first setting the hypotenuse to the radius, the second with a vertical side tangent to the circle at x = ±1 and the third with the horizontal side tangent to the circle at y = ±1 (you can use similarity and Pythagoras to get all the standard identities like tan = sin/cos, etc.)

⸻

1. I kind of did a speed run through high school math, taking essentially 5+ years of math in three years, so it’s likely that I ended up missing/glossing over stuff that people who were learning at a more rational pace did learn, although I think some of my teachers were too intimidated by me to try actually teaching me, much to my detriment.

[epgui]

Weird, in Canada (at least some provinces) I think that's a pretty standard part of both high school and undergraduate maths.

[dhosek]

The relationships between the functions are pretty standardly taught, but their derivation from the right triangles on the unit circle less so (other than sin and cos).

[cyber_kinetist]

The inequality stuff is just typical math olympiad material. Needed for solving olympiad problems, but doesn't matter that much for your overall math education from college and beyond.