To help remember the angles of the unit circle and their radian measures, it helps to use your hands and perhaps your musical talents.
Since we have five angles to learn in the first quadrant and most likely five fingers, let’s label the back of a left hand according to the Unit Circle.
Then mentally sing to the tune of Frere Jacques:
Left hand thumbkin, left hand thumbkin, 0 degrees, 0 degrees, on a unit circle, on a unit circle, 0 pi, 0 pi.
Left hand pointy, left hand pointy, 30 degrees, 30 degrees, on a unit circle, on a unit circle, pi over 6, pi over 6.
Left hand big boy, left hand big boy, 45 degrees, 45 degrees, on a unit circle, on a unit circle pi over 4, pi over 4.
Left hand ring finger, left hand ring finger, 60 degrees, 60 degrees, on a unit circle, on a unit circle, pi over 3, pi over 3.
Left hand pinky, left hand pinky, 90 degrees, 90 degrees, on a unit circle, on a unit circle, pi over 2, pi over 2.
Next label the fingers on the back of your right hand to match the angles in the second quadrant.
Mentally sing the next verse, but this time it’s right hand pinky that’s 90 degrees, and so on.
The third quadrant uses the right palm as in the photo below.
The song continues as right palm thumbkin…
Finally, the left palm is used for the 4th quadrant angles.
Finish the song with left palm pinky at 270 degrees, etc.
Sometimes the silliest of things makes the most reliable memories.