Euler's formula got me through a bunch of EE classes back when I was a student. I was pathologically unable to commit trig identities to memory, possibly due to laziness. So instead I learned Euler's formula and worked everything through in complex numbers until I was ready to give an answer. I never got marked down for it.
I did this exact same thing for math competitions. You often need some stupid exact formula that you are supposed to have memorized, but I never did.
De Moivre also yields the same results for this, and it's somewhat easier/faster to use.
