No real solution
I think you had the right idea in starting this thread, but you're assuming alot. I think only Brewnog touched upon this, which everyone else passed over. What you are assuming is that we have the time to implement these solutions. Do we though?
40% of our (United States)...
They should have told you exactly what type of lock this was. I assume koroljov's approach is correct for a type of lock that you would find on a http://www.hevanet.com/gillesp/briefcase-lock.JPG a student would put on their locker at school, which changes things. In that case, you would...
Supposing I need to solve a problem like: sec(arctan 2) or cos(2arcsin(5/13)), is there a method I could use that would not require a calculator? What I mean is that for an example like tan(arccos .5), the answer is "simple" because I know the arc cosine of .5 is pi/3 and then the tan of pi/3 is...