Quote:
Originally Posted by Stuck686 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