Doesn't take long to manually do it if you don't wanna memorize all the values. The timing on qr is more like if you can see a prob and know how to do it. I feel like the benefits of shaving a second or 2 by not using calculator or by memorizing all 16 values of the unit circle are marginal at best.
You should definitely google the "Unit circle left hand trick". I learned it in high school and it makes the unit circle trivial. As long as you can recognize when sin, cos and tan are positive or negative.