The peak of the full moon occurs, on average, every 29.53 days, and the approximate value of the moon that is lit can be modeled by a sinusoid. assume that all of the moon is lit at the peak of the full moon and that none of the moon is lit at the apex of the new moon. if the peak of the full moon was at 8 pm on august 24, what decimal value, , of the moon will be lit at midnight on october 12 of the same year?