I'm doing some trigonometry and am answering a question about the unit circle. In one question, I want to prelude my answer with an intuition. This leads me to the question:
Are there mathematical symbol for high and low? (I'm a bit lazy to write "high" and "low"). If there aren't, any suggestions?
Example (I'm obviously handwaving, and I'm not sure to what extent the example is even correct, it is just for the context of using the symbol):
In words: I want to show that a high to very high x-coordinate value in the 1st quadrant of the unit circle is a low to very low x-coordinate value when added with $\pi/2$ as that is a 90 degree anti-clockwise rotation (see the image for an example where x is high but not very high). For y the opposite is the case.
Mathematically I'd write:
$$P(cos(high\ x), sin(low\ y)$$ (note: my textbook says that $cos(\theta)$ is the x-coordinate for a point on the unit circle, because of this I feel comfortable leaving $\theta$ out of it and just overload the meaning of x with x-coordinate and with angle of x-coordinate, vice-versa for y. When I program in Java I do it all the time, here as well, I wouldn't do this if I'd need to communicate this to someone else but this example was written to myself only, I wouldn't use a high or low symbol in the first place if I'd write to someone else, but I'd like a shorthand for myself that has some historical backing to it)
$$Q = \pi/2 + P = 90\ degrees\ {anti-clockwise} + P$$
$$\text{So } Q(-sin(low\ y), cos(high\ x))$$
In visualization: $P = B, Q = C$ (I never used the GeoGebra viz tool before).
Visualization:
(I'll accept this answer within a month from now if no one is going to answer it, I invite Blue to write an answer)
Based on the comment one potential way to do this is stating something like:
Let there be two angles $x, y | x > 10y$.
For cognitive clarity (i.e. reducing cognitive load), it'd be smarter to use $a$ and $z$ as variables, such that you can more easily recognize the high and low value.
Let there be two angles $a, z | 10a < z$.
This means the same, but my brain intuitively gets it more. And since math notation is based to some extent on context with the purpose to aid ones memory, I think this is a slightly better way to write it down.
If one were to communicate to other people, I'd write:
$\theta_a, \theta_z | 10\theta_a < \theta_z$