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Replies: 8   Last Post: Apr 16, 1997 11:33 PM

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Wayne Murrah

Posts: 31
Registered: 12/3/04
Posted: Apr 16, 1997 12:46 AM
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I agree that it represents one unit arc length, but I don't consider it a
unit in the sense that degrees are. Radians are a non-unit in the sense
that you can include them when convenient, that is, whenever you want to
flag a number as representing an angle measure, but you can exclude them
whenever you don't want to complicate the units in your result of a
calculation. In dimensional analysis in science, for example, you can
either include or exclude radians where ever convenient, with accurate
results either way. The square of 30 degrees is 900 square degrees
(nonsense), but the square of 2 radians is 4, which is equivalent to 4
radians, by the way. If you want to approximate the sin (30 deg) using the
3rd order Taylor polynomial x-x^3/3!, using degrees is ridiculous (cubic
degrees?!?!), but if you substitute pi/6 radians, and choose to OMIT the
NON-UNIT "radian", the result is the appropriate, NON-UNIT decimal
approximation of the sin value (with NO radians and certainly no cubic
radians in the result).
>At 9:29 PM -0500 4/13/97, Wayne wrote:
>>One of the real values of radians is that it is a non-unit "unit" (since it
>>is the ratio of an arc length to the radius of a circle).

>I disagree. The radian is its own unit. One radian measures one unit of arc
>length on the unit circle.
>Jerry Uhl
>Professor of Mathematics 1409 West Green Street
>University of Illinois Urbana,Illinois 61801

Wayne Murrah
Porter-Gaud School
Charleston, SC


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