When the DFT is defined and described I typically see the basis functions described as an integral number of sine and cosine waves.
But the basis functions are $\sin(2\pi k (n/N))$ or $\cos(2\pi k(n/N))$ where $k$ is the harmonic, $N$ is the number of samples, $n$ is the time domain sample number.
So the right hand boundary of this argument is $2\pi k(N-1)/N$, which seems to be always a bit short of a full cycle.
Could someone please confirm or explain my error?
The picture below shows a sine basis function, apparently ending short of a full cycle.