[Potironette]

So..arcsin and arccos need to be functions because functions are more useful than relations (I think that's what they're called?) since those give just one output. Or maybe when a function gets inversed(?) people like them to remain functions and so limit them..? That doesn't really seem it though.
(if I just plot x = sin(y) or x = cos(y) I get a relation on desmos)
On the other hand, arctan can go on forever in the x direction and still give one output/be a function which is why they get to go on forever?

The bit about the video games was really interesting :o. Although, though I have a sense that angles are useful in video games I don't really know why figuring out an angle based on a coordinate would be useful.


I found this in my review sheet but I have no clue what it means:
Regular division: p = qd + r, r < d (dividend = quotient x divisor + remainder)
p(x) = q(x)d(x) + r(x) deg(r) < deg(d)

Taking d(x) = x - x_0,
p(x_0) = 0 <-> r(x_0) = 0 <-> p(x) = (x - x_0)q(x), i.e., (x - x_0)|p(x)

(It's the "Taking" part I don't understand. I'm pretty sure deg(r) < deg(d) is something about how remainders don't have the same "degree" as divisors(?), though I don't really know what a "degree" is. I used "<->" to replace the arrows in my review sheet. I'm not sure what "|" is supposed to be, though I vaguely remember reading somewhere it means "divides")


EDIT: Below those equations on dividing, the Remainder Theorem, Factor Theorem, Fundamental Theorem of Arithmetic, Fundamental Theorem of Algebra, and Rational Root Theorem are listed out...and they all refer to p(x) = (x - x_0)q(x). I guess it means to say that somehow, x - x_0 got rid of the remainder, somehow.?