The video that was posted on YouTube by @Edward Yuen
seemed somewhat self-serving to me, plus I didn't really see how he actually proved
the ninety-degree voltage vs current relationship for sinusoidal wave forms applied to a capacitor. This was "experimentally verified" with only three discrete frequencies in a video that lasted ten and a half minutes. More than anything else the video seemed to be a showcase for a digital storage oscilloscope and a signal generator. Maybe if I put on a set of head-phones and played the video again with sound it would make more sense. However, I trust the math and the theory of how capacitors and inductors work and use actual components when I want to build something.
BTW, the classic way of demonstrating the current vs voltage relationship in capacitors, as well as inductors, is with a Lissajous pattern on an X-Y oscilloscope display.