As a young kid doing qbasic, everything moving around on the screen was x/y/xchng/ychng. The watershed moment for me was in highschool and suddenly recognizing that sin/cos were how to get from polar to cartesian, and atan2 was how to go the other direction. A week later my little platforming arena shooter had heat-seeking missiles in it.

I think a big part of the problem is a failure to emphasize the right stuff. I always see trigonometry presented in terms of all six functions and arcfunctions and the relationships between them— this is a bunch of abstract stuff that most people don't care about and will never need; it's nuts to present all of this at once when the small piece of it needed for polar coordinate operations is so immediately and obviously useful.