RE: [MATHEDCC] Why radians?

kschmid@UWC.EDU
Mon, 1 Nov 1999 12:32:07 -0600

Martin,
Whenever I get the inquiry about why we use radians, the simplest
way to answer that beginning user is to ask them to find the length of arc
of a circle of radius 3 subtended by a central angle of 13 degrees (or use
some other numbers that aren't factors of 360). The point soon becomes
quite clear that if the central angle is defined as the ratio of arc to
radius, life is simpler and more meaningful.
Another nice example is to simply ask them to graph y = x - sin(x)
and make some sense of it. It is a nice way to see that for x >= 0, y is
positive, but not by much for small x, which shows why linear approximation
works so well near x = 0.
You might have some other good ways to get the point across, but
these have worked for me.

Karl

-----Original Message-----
From: Martin Kalmar [mailto:MKalmar@fcc.cc.md.us]
Sent: Monday, November 01, 1999 11:22 AM
To: Mathedcc@archives.math.utk.edu
Subject: [MATHEDCC] Why radians?

When students ask (not often enough) why do we need to measure angles in
radians, I know of no other answer than it makes things very convenient in
calculus. This is fine for my calculus students who can see what the
derivatives of trig functions would look like without radians, but what
other answer can I give my pre-calculus students?

Does anyone know of other good reasons for using radians?

Does anyone know the history of radian measure? Who first used it and why?

Martin Kalmar
Frederick Community College
Frederick, Md.
mkalmar@fcc.cc.md.us

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