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Date: 03/22/2001 at 19:12:41

Dr. Math -

I have searched everywhere for the history behind radians. Why is it
that they replaced degrees? Is there a history behind this? I thought
it was because of the ability to have zero degrees in a circle, but I
don't think this is the reason.
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Date: 03/22/2001 at 22:56:45
From: Doctor Peterson

I wouldn't exactly say that radians replaced degrees - degrees are
still very much in use. Each has its place: degrees work well for
naming common angles with whole numbers (30, 45, 60, 90, rather than
pi/6, etc.), while radians work well in calculus. You can find several
explanations of the latter by searching our archives for the words

http://mathforum.org/dr.math/problems/munroe12.3.97.html

The basic idea is that radians measure the arc length of an angle,
which for small angles is close to the sine. That means that if you
measure angles in radians, the slope of the graph of the sine is 1 at
the origin. When you get to calculus, you find that the derivative of
the sine is the cosine - it wouldn't be nearly as simple using
degrees. And you can write infinite series and other formulas that
give the value of the sine, which are much simpler using radians.
Radians simply turn out to be the "obvious" unit to use for angles,
once you've had plenty of experience with them.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
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Associated Topics:
High School Trigonometry
Middle School Terms/Units of Measurement

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