This problem follows on from Going Round in Circles.
Watch the film below.

Full Screen Version
This text is usually replaced by the Flash movie.

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 .