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'Where Is the Dot?' printed from https://nrich.maths.org/

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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 $90^{\circ}$ 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?