Path: utzoo!attcan!uunet!decwrl!bacchus.pa.dec.com!shlump.nac.dec.com!jareth.enet.dec.com!edp
From: edp@jareth.enet.dec.com (Eric Postpischil (Always mount a scratch monkey.))
Newsgroups: comp.sys.handhelds
Subject: Re: A strange feature (a bug?)
Keywords: symbolic integration/differentation in DEG mode
Message-ID: <15954@shlump.nac.dec.com>
Date: 10 Oct 90 19:48:06 GMT
References: <1990Oct10.152505.2903@wuarchive.wustl.edu> <1990Oct10.093506.8848@wuarchive.wustl.edu> <15930@shlump.nac.dec.com>
Sender: newsdaemon@shlump.nac.dec.com
Reply-To: edp@jareth.enet.dec.com (Eric Postpischil (Always mount a scratch monkey.))
Organization: Digital Equipment Corporation
Lines: 33

In article <1990Oct10.152505.2903@wuarchive.wustl.edu> Povl writes:

>60 degress = pi/3 radians. This is a FACT!
>thus  sin( 60deg ) = sin( pi/3 RAD )
>these two point are exactly at the same point on the curve, and thus
>the derivative must also be the same. 

The last sentence is incorrect, and the sentence preceding it is imprecise.

If you plot y = sin(x degrees), you will get a different graph than if you plot
y=sin(x radians).
The former graph will be more spread out than the latter.  The slopes will be
lesser in magnitude.

On the plot of y=sin(x radians), pi/3 radians is represented at the coordinate
(pi/3, sqrt(3)/2).  On the plot of y=sin(x degrees), 60 degrees is represented
at the coordinate (60, sqrt(3)/2).

They are different points.  They are on different curves.  They have different
slopes.

Observe that when you take the derivative of sin(x degrees) or sin(x radians),
you are NOT taking the derivative with respect to an angle; you are taking the
derivative with respect to x -- a variable which is scaled by degrees or radians
before being fed to the sine function.

If you don't believe it, then actually physically draw the curves, plotting the
sine 0, 10, 20, 30, 40, 50, 60, 70, 80, and 90 degrees at places where x = 0,
10, 20, et cetera.  Then plot the sine for x in radians.  You'll get different
curves, and you will see the different slope.


				-- edp