How Can We Alter a Sine Wave to Only Intercept sin(x) Once?

This is a rather different video on this channel, as instead of some sort of gameplay or cinematic-type video, it's a math video. Why is that? Well, I've sort of fallen out of the interest with gaming related videos, my cinematic videos won't stop, however, one subject I'm good at is math, so I figured I may as well share my love for math with some videos I post! It is surprisingly fun to make these videos.

The topic of this video was brought up in my Geometry class, I remember finding a problem such as this and I found the solution to be so satisfying to find, because surely a sine wave is bound to intercept another transformed wave eventually, right? But no! It completely defies normal expectations of a repeating function, and I thought that was fascinating and I decided to try making a video to explain it simply to see if I could. I hope anyone watching may like this video, also; for any viewers on PC, the video was rendered in 9:16, with the target being people on a mobile phone of some sort, which is also why I kept the video seldomly short. However, if people like this sort of video, I may as well make more and make them longer too!

Speaking of the Music...
"Run Part 2" - Andrew Applepie
"Graze the Roof" - Laura Shigihara
"Fractals" - Vincent Rubinetti
"Moon Men(Instrumental)" - Jake Chudnow
"Hypothesis" - Vincent Rubinetti