I'll do my best to explain, but what this really comes down to is trigonometry. What I'm about to explain I was never personally taught in school, but maybe you had better teachers than me ¯\_(ツ)_/¯. Right, so depending on where in the world you are from you might have heard this mnemonic phrase for memorizing the definitions of the trigonometric functions sine, cosine, and tangent: SOH-CAH-TOA It stands for: SOH => Sine = Opposite/Hypotenuse CAH => Cosine = Adjacent/Hypotenuse TOA => Tangent = Opposite/Adjacent Now you may know this, but I didn't: Sine and cosine are actually percentages (trig values in general are). They can be from -100% to 100%. This might lead you to ask why? That's because absolute values in trig really don't have meaning to them. What do I mean by this? Say I told you I invested money in a bond and got $50 back. You have no idea if that was a good investment or not because I only told you the absolute return I got. Say instead I told you I got a 80% increase from my bond and you know I got a dope deal. It's the same with trig. We need a general way of being able to discern width, height, and other values. We do this via percentages. If I take my right triangle and scale all the lengths in it so that the hypotenuse is indexed with a length of one then my sine value represents the height of the triangle, and my cosine represents the width. / | 1 / | / | Sin(Θ) /Θ__| Cos(Θ) Try it out: Sin^2(Θ) + Cos^2(Θ) = 1 (based on Pythagorean theorem) Intuitively the mnemonic above should make sense then. We know we can find sine by taking any right triangle and dividing it's height (opposite) by it's hypotenuse to get the height of the triangle scaled to a unit circle. In a similar sense we can take the width (adjacent) and divide by the hypotenuse to get the cosine (width) of the triangle scaled to a unit circle. Hopefully, you can see that once we have the width and height in percentage form like this it is very easy to scale the triangle by adjusting the hypotenuse and working backwards to get an infinite number of similar triangles with different widths and heights (AKA the same angle). It also works a similar way. Given that we know the angle of the triangle we can find the percentage that the width and the height should be in a given right triangle. As such in the video above we are taking this concept and applying it to vectors in space. We already know the direction of the width (right vector) and the height (up vector) so we are simply scaling them with sine and cosine then adding together to find where the hypotenuse vector would be given an arbitrary angle. We just need to make sure that the right and up vector are the same length (magnitude) so that the radius of the circle we are tracing is consistent throughout. Hopefully that cleared things up, if not all I can suggest is trying to play around with it on geogebra or something.

100% agree on the beginning being useless shit haha. In the more recent things I've posted (regarding explaining math stuff) I prefer to do so through text. It helps me provide more detailed better thought out explanations. I know you already watched the video, but here's a post I made on the same topic but written: github.com/EgoMoose/Articles/blob/master/Rodrigues'%20rotation/Rodrigues'%20rotation.md Not all, but a lot of the topics I cover on this channel + more are in that repository in written form. Thanks for the feedback though! :)