002.1 Phases of the Moon
The "First Quarter Moon" shows half of the surface and is visible from sunset until it sets at midnight.
Suppose that you want to look for the first quarter Moon at around noon. It does not stand out much against the day sky, so you need to know where to look. Where is it?
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Since it is noon, the Sun is at its highest point and directly South of you. The quarter Moon will be rising in the East at that moment, so face the Sun and then turn a quarter turn to the left and you should see the quarter moon low on the horizon.