120v and 240v are both full sine wave, the difference is that the two legs of 240v are 180 degrees out of phase with the same zero reference. so when you reference either leg to ground you get 120v as the peak of the sine wave going either positive or negative. For 240v you are measuring across both legs so while one leg is peaking in the positive direction the other is peaking in the negative direction giving a total of 240 across both but 120 to the zero reference which is ground. Then the cycle reverses and the one that was positive goes negative, etc, and you get the same 240v. It's a sine wave because that's what an electrical AC generator produces, and what transformers are most efficient running. But there is no gap in voltage, just the zero crossover point. Power factor is an average .707 of peak voltage.
HTH
Jim