1. The problem statement, all variables and given/known data Is there any difference between the vector space spanned by the set cos(t),sin(t) and the vector space spanned by the set cos(t)+sin(t),cos(t)-sin(t)? 2. Relevant equations 3. The attempt at a solution Not really a homework question but it will help me answer a problem set given to me by my teacher. I would have to guess that the answer is that there is no difference because of the behavior of sin. if it begins at any place on a number line it doesn't matter if its going in the positive or negative direction, it will still travel the other way in the manor that of which if its sign was reversed.... im sorry if that doesn't make sense. I hope someone who reads this will understand what I mean.