This looks like it should be really simple, but unfortunately I'm not quickly understanding the basic lessons I've looked over. I have two simple sine curves here, with periods $p_1$ and $p_2$ (I'm prepared to be wrong on my terminology and notation): $$ x = \cos ( x \cdot p_1 ) \qquad x = \sin ( x \cdot p_2 ) \\ p_1 = 94.247 \qquad p_2 = 1.5707\\ 0 \le x \le 1 \quad -1 \le y \le 1 $$ I'm trying to combine them such that the resulting curve's amplitude is limited near $0$ at the start and has gradually increasing amplitude until it reaches $1$. The second curve is just an unimportant guiding behavior and seems final, but I'll still be adjusting the period of the first curve $(p_1)$ for more changes. (I don't know how I was supposed to arrive at the period multipliers, but that's not important, the trial-and-error values work fine)
I've been working with curve editors for years, being mindful of the trigonometry behind it. But I haven't had use for the equations in 12 years, I couldn't even remember how to graph and adjust a sine wave. I'm sorry if it looks a bit negligent asking for answers on something basic, but I've spent 12 total hours across 2 days getting this far, on what I was only supposed to spend 2 hours on. I did at least figure out getting values I need by working with $x = \frac{ 2 \pi \arccos ( y )} p $
Have a good day!
Appended sketch: https://i.imgur.com/7bJqpH7.jpg
