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Old April 2nd, 2007, 11:59 AM
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Quote:
Originally Posted by Stuck686 View Post
1) what angle pheta is measured by a 7inch arc on a circle of radius=3
Find: Radians=
Degrees=
revs=
Thanks in advance
Ok, first off, its "theta" not "pheta," i don't really mind misspellings, as long as you can get what the person is trying to say, but apparently a lot of people here do, see Spelling

Ok, the formula for length of arc in radians is:
s = r@

where s is the arc length, r is the radius, and @ is supposed to be the symbol theta, which is measured in radians.

the formula for arc length in degrees is
s = @/360 * 2pi*r

we won't need both formulas, one is enough. let's use the radian formula since its simpler.

s = r@
=> @ = s/r
if s=7, r = 3
@ = 7/3 radians

now to convert from radians to degrees, we multiply by 180/pi
so @ = 7/3 * 180/pi = 420/pi degrees

but how many did we make? we can use either the radians or degrees to find out

Using degrees, Revs = (420/pi)/360 = 7/6pi revs = 0.371 revs

or

Using radians, Revs = (7/3)/2pi = 7/6pi revs = 0.371 revs
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