Figure: An illustration of the lunar phases in order and the Moon's position relative to the Earth

Caption: A diagram illustrating the lunar phases (i.e., the phases of the Moon) over the course of a lunar month = 29.530588861 days (mean J2000) ≅ 29.53059 days (mean J2000 to 7 digits) ≅ 29.5 days.

Features:

1. lunar phases of the in time order are:
   1. new moon: The Moon is in conjunction with the Sun when projected onto the ecliptic plane, but NOT in space, except during solar eclipses.
   2. waxing crescent moon: The Moon is east of the Sun in the angular range 0°--90°.
   3. 1st quarter moon: The Moon is in eastern quadrature: i.e., 90° east of the Sun.
   4. waxing gibbous moon: The Moon is east of the Sun in the angular range 90°--180°.
   5. full moon: The Moon is in oppositions to the Sun when projected onto the ecliptic plane, but NOT in space, except during lunar eclipses.
   6. waning gibbous moon: The Moon is west of the Sun in the angular range 90°--180°.
   7. 3rd quarter moon or last quarter moon: The Moon is in western quadrature: i.e., 90° west of the Sun.
   8. waning crescent moon: The Moon is west of the Sun in the angular range 0°--90°.
   9. new moon: The cycle of lunar phases restarts.

      And one also has the abbreviated expressions:

   10. waxing moon
   11. waning moon
   12. crescent moon
   13. gibbous moon
   14. half moon which is either of 1st quarter moon or 3rd quarter moon---which is not contradictory---"half" describes how much of the Moon is illuminated and "quarter" helps tell what the fraction of the lunar month has passed.

2. To "wax" (NOT used in the sense of coating in wax) is a nearly obsolete verb in English meaning "to grow". It is now used almost exclusively for the waxing of the Moon.
   To wax is probably cognate to wachsen, the common German verb meaning "to grow".

   You see English and German are mutually intelligible---and you can understand Swedish too---if you really, really try.

3. "Gibbous" means convex or protuberant and is used almost exclusively nowadays in describing the gibbous moon.

4. The diagram is not-to-scale ---the Earth-Moon distance is about 60 Earth radii recall. The bend in the Earth's orbit is unreal.

5. The dotted circle around the Earth shows the Moon's orbit.

6. The long-dash-short-dash grey line approximately illustrates moon's trajectory in space.

7. The solid white line passing through the Earth represents Earth's orbit around the Sun. Note the word "represents": the Earth's orbit does NOT have a funny bend in it.