Let $V$ be the linear span of the functions $1,cos(x),sin(x)$. Let the operator $T$ on $V$ be given by the rule $Ty(x)=y(x+ \pi/4)$. Find the eigenvalues and eigenvectors of T in V.
I know how to find the eigenvalues and eigenvectors for a matrix, but I do not know how to find them in this situation.