# M-point FFT Amplitude of N-samples of a sinusoid

Suppose you have N samples of a sinusoid of frequency $f_0$.

$$x[n] = A\sin[2\pi (f_0/f_s)n ]$$

Suppose you take an M-point FFT (where M may be greater than N) of your N samples of x. What will the amplitude of the peak of the spectrum be?