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Re: vector directions



In a similar vein, I encourage my students to almost exclusively use the
cosine function when forming vector components. I have them write the
angle between the vector and both the x and y axes - then use the cosine
for the side adjacent to each of those angles. I place no preference on
referring to the x axis versus the y. This approach pays dividends when
dealing with inclined ramps, where it is very ambiguous as to what is
the best placement of axes and where the sines and cosines mysteriously
swap in the usual treatment that places the x axis parallel to the ramp.

bob at PC

Dan Crowe wrote:

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 the
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=
ct
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