The moon is still fairly high in the sky this morning. It’s in the Third Quarter phase, also known as the Last Quarter Moon. This phase occurs about three weeks after the New Moon and is so-called because the Moon is three-quarters of the way through its orbit around the Earth, in case you were wondering, because obviously it looks like “half a moon”.
The Moon will have risen at about midnight last night from the eastern horizon and will set in the west at about midday. Next New Moon will be 15th February.