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This problem follows on from Going Round in Circles.
Watch the film below.
Imagine the dot starts at the point $(1,0)$, turns through $60$ degrees anticlockwise and then stops.
I was wondering, if the point hadn't stopped, and instead carried on until it had turned through $30$ $000$ degrees, might it have finished the same distance above the horizontal axis?
I took out my calculator and typed $30$ $000$ $\div$ $360$
The answer on the screen was $83.333333$.
How can I use this to help me solve my problem?
There are ideas for follow-up problems in the Notes .