The key thing with most trig calculations is to recognize how things relate to each other -- visualization is key, rather than rote memorization.Yes, I agree totally!Sure, it may take 3 seconds longer to visualize things, but it takes you to the real nature of the problem, and saves you from disastrous "sin vs. cos vs. tan" mistakes. I always have Big Chief Sohcahtoa review my analysis before committing to an answer!
But I just do that for trig. equations. To do that for simple multiplication or division - as per what you advocate - is just insane.