Because it's for implicit equations as opposed to explicit equations of the form y=f(x)

Literally just came across this the other day
youtu.be/oIhdrMh3UJw

The main other ones I'd drawn attention to are probably sin(0)=tan(0)=0 and cos(0)=1 for y-intercepts and because they show up in integrals regularly, and I want to make sure students don't mistake e^0=cos(0)=1 with being 0 which happens frequently.

We usually have already got that sin(45)=cos(45)=1√/2 by osmosis, but making that explicit (useful for intersections too)

We use the fact that tan is increasing from 1/√3 to 1 to √3 for 30 to 45 to 60° to help differentiate those.

That basically leaves sin(60)=cos(30)=√3/2 and the multiples of 90

After they've been getting familiar with those and we're trying to improve efficiency, we start memorising the rational ones in tri's: sin(30)=cos(60)=½, tan(45)=1 (because rational tends to feel easier to remember)

I'm in the same boat. I call them the half-square and half-equilateral triangle to help Ss remember how to construct the tri's if they forget.

I also use the unit circle definitions (x, y coordinates for cosine and sine and gradient of radius or length of tangent to x-axis) for the multiples of 90

We only do x^2, log x, and 1/x, so it's a fairly short ladder. But it was /so/ much easier to remember how to label the circle.

Yes, I can do it by considering similarities to the respective graphs, but this subject doesn't go through that.

I think I love it even more than discorectangle

I've discovered some people call it a convex angle, which makes some sense, although it suggests a reflex angle should be called concave.
Incidentally, did you know that angles that add uo to 360° are called explementary?

Explementary is such a handy word

easy change

the (hopefully) fully corrected version and x^n

First principles, yeah, heaps. By factorising rather than expanding? Surprisingly, no!

This was wrong too, lol #OnARoll

Doesn't surprise me

Queries:
1. Are the two methods actually distinct and have been inadvertently conflated somewhere along the line?
2. Which (if either) should be favoured as an introductory/straight-forward/trend-agnostic method?

Additional example over 2 years, quarterly.

They're out JUST enough that you could get marked incorrectly from an assumption of one method or the other because it looks like a rounding error