If you use degrees in equations like s = r * theta for arc length on a
circle, your answers will always be off by a factor of ( pi / 180 ). In
calculating frequencies for motion the same phenomenon also occurs. Radians
are truly unitless measures of a fractional part of the arc of the circle to
the total circumference. In time units they are a fractional part of the
time needed to complete part of a rotation along the arc on a circle
compared to the total period of one complete rotation about the circle.
There is truly no unit of measure "radian". It is a pure number. Degrees,
however, are a unit of measure and conversions must be used to remove the
units.
David Beach
Labette Community College
Parsons, KS
> ----------
> From: Martin Kalmar[SMTP:MKalmar@fcc.cc.md.us]
> Reply To: Martin Kalmar
> 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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