as a calculus and physics teacher, I would say very important.
So, I'm pretty far in the semester ( actually was three weeks ahead of class and took all that time studying for my midterm ) and have come to a point in my book where it's assuming I've memorized function values for 30, 45, 60, and 90 degree angles as well as the measure of those angles in radians, etc.
I've just been, whenever I come across the problems, letting my calculator give me values for them. ( It gives me exact values, love my TI-89 )
I never memorized multiplication tables nor any of the brute-force memorization stuff. On my recent midterm for the first page I re-built the pythagorean identities from a^2+b^2=c^2 and my linear and angular speed formulas.
How important will it be for me to have memorized the function values of these angles later on in calculus and such?