At what times of the day or night does the first quarter moon rise above the
horizon, transit (reach its highest elevation in the sky, almost directly
overhead), and set?
Let's take a look at a single day when the Moon is in the first quarter
phase, as drawn in the figure shown in slide #14.
When the moon is located below the Earth in the figure (at the bottom edge of
the figure), it is half-illuminated by the Sun and lies in the first quarter
phase.
At what time of the day or night does the person shown on the Earth pass
underneath this first quarter Moon? (This is when the Moon appears
highest in the sky, as it transits.)
At what times of the day or night does the first quarter moon rise, transit,
and set?
The person shown on the figure passes underneath the first quarter moon at
dusk, around 6 pm.
Because the Earth spins once on its own axis every day (every 24 hours), both
the Sun and the Moon spend about twelve hours above the horizon and twelve
hours hidden below it.