1. The problem statement, all variables and given/known data what is cos(2n*pi) 2. Relevant equations 3. The attempt at a solution I understand that cos(npi)=(-1)^n so is cos(2n*pi)=2(-1)^n ??
...I think it is necessary to know the graph of cos(x), which may help a lot. so, find one. edit (:shy: trying not to be ambiguous) ...I think it is necessary for one to know the graph of cos(x), which may also help a lot. (regardless of this particular problem)... "periodic" is really the key
It might help. It is not necessary. All that is necessary is to know what "periodic" means. No computation is required.
I understand that periodic means that cosine function repeats after multiples of 2 pi. but how would that have anything to do with writing cos(2n*pi) ? cos (npi)=(-1)^n because as long as n is an integer, the value will alternate from -1 and 1 (clearly form the graph)
Would it be easier if it were written n*(2pi) rather than 2n*pi? This is about multiples of 2pi! cos(2pi)= cos(0+ 2pi)= cos(0)= 1 cos(4pi)= cos(2pi+ 2pi)= cos(2pi)= 1 cos(6pi)= cos(4pi+ 2pi)= cos(4pi)= 1
oh right!!! so cos(n2pi) has to always be 1...i feel very stupid, i should have known that. for all n, cos(2npi) must be 1 as long as n is an integer. thank you very much