Huh ? You do realise that the apparent motion of the moon over a given day is because of the rotation of the earth, and that the changes in the relative positions of the sun and moon, and hence the lighting conditions of the moon, are negligible ?
Which is just the definition of a half moon (technically called a quarter moon). Which is why it's really weird to be asking "what if a full moon were at 90⁰ from you compared to the sun?"