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Re: RADIAN MEASURE
Posted:
Apr 16, 1997 12:46 AM


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 nonunit 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 xx^3/3!, using degrees is ridiculous (cubic degrees?!?!), but if you substitute pi/6 radians, and choose to OMIT the NONUNIT "radian", the result is the appropriate, NONUNIT 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 nonunit "unit" (since it >>is the ratio of an arc length to the radius of a circle). > >Wayne >I disagree. The radian is its own unit. One radian measures one unit of arc >length on the unit circle. >Jerry > > > >Jerry Uhl juhl@ncsa.uiuc.edu >Professor of Mathematics 1409 West Green Street >University of Illinois Urbana,Illinois 61801
Wayne Murrah PorterGaud School Charleston, SC
School: wayne.murrah@portergaud.edu Home: wmurrah@awod.com



