The following is an excerpt from an email I wrote to one of my past math professors today:
Normally when I'm sailing I do lots of navigation work by hand. I find our position via celestial means, I calculate the time based on the position of the moon in the sky, and I find our course and speed using trig tables and formulae in the methods that have been used for hundreds of years. This trip I've had to stop doing all spherical trig / navigation related mathematics (and just let the computers do it for me) since in navigation we measure angles from north counting in degrees to the right, but in trig we measure them from east counting in radians to the left. Switching between the two every day proved to be my limit...one day on watch I stuttered in giving a helm order because the new course was exactly 315 degrees and I kept wanting to say "three pi over four". You will notice, strictly speaking, 315 degrees does not equal 3pi/4 radians, but they both end up being the same thing when you measure from north v. east and count to the right v. left. Finally they both end up being "north west" if you like.