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Age 14 to 16
Challenge Level
Watch the film below.
Imagine the dot starts at the point $(1,0)$ and turns anticlockwise.
Estimate the height of the dot above the horizontal axis after it has turned through $45^\circ$.
Estimate the angle that the dot needs to turn in order to be exactly $0.5$ units above the horizontal axis.
Show how you can use Pythagoras' Theorem to calculate the height of the dot above the horizontal axis after it has turned through $45^\circ$.
Again, without resorting to Trigonometry, calculate the height of the dot above the horizontal axis after it has turned through $30^\circ$ and $60^\circ$?
Are there any other angles for which you can calculate the height of the dot above the horizontal axis?
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.