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I agree with Joel. Only when measuring angular displacement in rotat=
ions is it necessary to consistently measure angles in the same direc=
tion from the same reference direction, and even then it isn't necess=
ary to always measure angles CCW from the positive x-axis.
Daniel Crowe
Oklahoma School of Science and Mathematics
Ardmore Regional Center
dcrowe@sotc.org
-----Original Message-----
=46rom: RAUBER, JOEL [mailto:JOEL_RAUBER@SDSTATE.EDU]
Sent: Friday, October 03, 2003 9:39 AM
To: PHYS-L@lists.nau.edu
Subject: Re: vector directions
Mike E. wrote in part:
=2E . .
Part of the problem stems from the fact that students tend to view =the
trig relationships from a right triangle perspective. If thect
vector is
-3i + 4j they are going to draw a right triangle in quadrant II and
solve for the angle of that triangle. Some of them won't
even get that
correct... they'll invert the 4/3 and find the arctan of 3/4.
Some will
include the minus sign and some won't. So we might get any of the
following answers... ( 53.1, -53.1, 36.9, -36.9 )... when the corre=
answer is 126.9 degrees.
=2E . .
The correct answer is 126.9 degrees only if you have defined the corr=
ect
answer to be the angle measured CCW from the positive x-axis.
Perhaps in a high school class that is fine.
However, I tell my students I'll accept any of the angles mentioned a=
bove if
they tell me unambigously how they are measuring the angles (relative=
to
what and what they are calling positive vs. negative angles) and if t=
heir
answer matches their fiducial statements.
If they don't tell me I tell them I'll grade according positive angle=
s being
measured CCW from the positive x-axis.
Joel R