Re: supplementary S.I. units

["Daniel L. MacIsaac" <Dan.MacIsaac@Nau.Edu>]

> On Fri, 25 Sep 1998, George Spagna wrote:
>
> > At 09:05 AM 9/25/98 -0400, Donald E. Simanek wrote:
> > > sin(theta) and tan(theta) approach theta radians in the limit as theta
> > > goes to zero. Not so if theta is measured in degrees.
> >
> > Oops - don't think you meant that the way it came out.  Sine and tangent
> > approach zero as theta approaches zero, no matter which set of units are
> > used for theta.  The size of the domain of theta over which the
> > approximation works well is certainly better in radians!
>
> Yep, careless use of the words "in the limit". Should have said "As theta
> gets small.
>
> 	-- Donald

....this is a great activity for spreadsheeting.  Answer the following
questions in your own words:

- for what small angles does sin(theta) look like theta in rad?
- how small for agreement within 5%?  1%?
- what DOES sin(theta)/theta in radians converge to for small angles?

- what DOES sin(theta)/theta in degrees converge to for small angles?
- can you interpret this number as a conversion constant?

- what does sin(theta)/theta in gradians converge to?
- can you interpret this number as a conversion constant?

- what does "a natural system of angular measurement" mean? 

See also Arons TEACHING INTRODUCTORY PHYSICS, p117(PtI).

Dan M

Dan MacIsaac, Assistant Professor of Physics and Astronomy, Northern AZ Univ
danmac@nau.edu  http://www.phy.nau.edu/~danmac