Round and Round and Round

This problem offers students an opportunity to test their understanding of division and to consider different ways in which calculators can be used.

The interactivity also offers students a chance to explore the relationships between the angles of turn that produce the same vertical and horizontal displacements.

Follow up questions could include:

Imagine the dot starts at the point $(1,0)$, turns through $20$ $000$ degrees anticlockwise and then stops.

Through what angle(s) between $0$ and $360$ degrees would the dot have had to turn if it was to finish the same distance above/below the horizontal axis?

If I type $20$ $000$ $\div$ $360$ into my calculator the answer on the screen is $55.555556$
How can this help me answer the question?

Similarly for $40$ $000$ degrees.
If I type $40$ $000$ $\div$ $360$ into my calculator the answer on the screen is $111.11111$.

Similarly for $80$ $000$ degrees.
If I type $80$ $000$ $\div$ $360$ into my calculator the answer on the screen is $222.22222$.

Similarly for $250$ $000$ degrees.
If I type $250$ $000$ $\div$ $360$ into my calculator the answer on the screen is $694.44444$.

And what about horizontal displacements to the left/right of the vertical axis?

Students could make up their own questions...