This problem offers students an opportunity to apply Pythagoras' Theorem.

It can also be used as a starting point for Trigonometry:

• what happens to the height of the dot during the first 90 degrees of turn?
• what happens to the height of the dot when it turns beyond 90 degrees?
• what can you say about the horizontal displacement of the dot as it turns through a full circle?

* what happens to the height of the dot during the first ${90}^{\circ }$ of turn?
* what happens to the height of the dot when it turns beyond ${90}^{\circ }$?
* what can you say about the horizontal displacement of the dot as it turns through a full circle?