Why Radians?

Date: 12/03/97 at 21:49:12
From: Christine Munroe
Subject: Trigonometry

Why use radians to measure angles over degrees?  Why should they be 
used, three reasons?  Why are they better?

Date: 12/04/97 at 08:41:07
From: Doctor Jerry
Subject: Re: Trigonometry

Hi Christine,

For surveyors, degrees are just as good as radians, although the 
complicated business of degrees, minutes, and seconds (based on 
conventions established by Babylonian astronomers, long, long ago) is 
something of a waste of time. For engineers, physicists, and other 
applied scientists who use calculus, radians are greatly preferred 
since they simplify many calculations. If you haven't had calculus, it 
is difficult to explain this comment, although here is a taste of the 
idea. In a circle of radius a and with central angle t measured in 
radians, the length of the intercepted arc is s = a*t. If the angle t 
is measured in degrees, the formula is s = a*t*(pi/180). For the same 
kinds of reasons, "natural" logarithms are preferred to base 10 
logarithms.

Radians are more naturally related to the measurement of angles 
since one radian is the angle intercepted by an arc whose length is 
one radius. This seems more natural to most of us than saying, well, 
1 degree is the 360th part of the circumference. Why not the 257th 
part?  Or, as some would like, the 100th part? 

-Doctor Jerry,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/