What is the orientation of: p = (3, -4)T ?
Plugging the numbers into the MS Windows calculator:
arc tan( y/x ) = arc tan( -4/3 ) = arc tan( -1.333333333333 ) = -53.13°
The calculation looks about right, in the diagram.
If you want the angle to be expressed as a counter-clockwise rotation,
then it is
Sadly, it looks like the vector -p will give you
the same result.
So what to do?
Always sketch the vector when you are computing its orientation.
Then you can see that the angle you want for -p
is
What is the orientation of u = (-4, -2)T ? (Sketch the vector first, then use a calculator.)