Re: vector directions

["RAUBER, JOEL" <JOEL_RAUBER@SDSTATE.EDU>]

Mike E. wrote in part:

. . .
> 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 correct
> answer is 126.9 degrees.

. . .

The correct answer is 126.9 degrees only if you have defined the correct
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 above 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 their
answer matches their fiducial statements.

If they don't tell me I tell them I'll grade according positive angles being
measured CCW from the positive x-axis.

Joel R