The math used is basic Trigonometry… Sounds like you are implying that you do not go to school? Sorry to hear. There are plenty of free resources to teach you what you need to know online.
You can try Grant Anderson’s lockdown course on YT… specifically relevant is Ep.2.:
Also useful is Sam Bowman’s Procedural Texture series. You can see Piranha4D’s progress following that course.
There is no “arch” - it’s just the rooted Cos function (that is multiplied with the noise (i.e. its used to “modulate” the noise)). Please follow the Desmos link and experiment with what I’ve provided to make this clear.
This is an understatement…
Good luck.