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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.