Cut-Off Sinusoid or Sinuosoid?? - Standing Voltage Waves on Transmission Lines
2-15 shows special cases of 2-14, i.e. open circuit and short circuit terminations. In 2-15 b,c the forward and reflected sinusoids are 180 deg out of phase at the given distances along the line, so they sum to zero.

Remember, the plots are of the sinusoidal amplitudes, not of the actual sinusoidal signals, so 'cutting the sine wave in half' is not what's happening. 

http://en.wikipedia.org/wiki/File:Standing_wave_2.gif