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/ |
Search the Dr. Math Library: |
[Privacy Policy] [Terms of Use]
Ask Dr. Math^{TM}
© 1994- The Math Forum at NCTM. All rights reserved.
http://mathforum.org/dr.math/