# trigonometry

how to express radians to degrees, minutes, and seconds?
how to express fractions to degrees, minutes, and seconds?
through how many radians does the hour hand of a watch turn in 5 hours? 1/2 hour? 10 minutes? 3 days? between 8 am and 5:30 pm?

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1. convert radians to degrees, as usual. Then multiply by 60 and 60 on the decimal parts:

23.461°
.461 * 60 = 27.66'
.66 * 60 = 40"
So, 23°27'40"

Do the reverse to go the other way. Divide by 60 and 3600 to convert ' and " to °.

Now use that knowledge along with the fact that 360° = 2pi radians.

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posted by Steve

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