John,

IF the sinewave were a pure sinewave (and that means zero dc offset, zero noise, zero circulating currents that cause slowly varying dc offsets and the frequency didn't vary so that you didn't have to correct for variation in period during the computation of the mean), then you could use a quarter cycle to estimate the rms amplitude. The mathematical reason can be found in the waveform symmetry.

Cutting to the chase, a quarter cycle of samples would be squared, summed and divided by one fourth of the sinewave period, then the square root taken.

But reality ain't like that, as San and Steve alluded to.

Bruce