arc tan( y/x ) = arc tan( 4/3 ) = arc tan( 1.333333333333 ) = 53.13°

The diagram shows the vector represented by **k** = (3, 4)^{T}.
Its orientation was calculated to be 53.13° to the positive x axis.
That looks about right.
The formula worked!

Now calculate the orientation of **-k** = (-3, -4)^{T}.

Plugging into the formula:

arc tan( y/x ) = arc tan( -4/-3 ) = arc tan( 4/3 ) = arc tan( 1.333333333333 ) = 53.13°

Hmm... something is wrong.
The formula gave us the same angle for a
vector pointing in the opposite direction to the first.
The problem is that information is lost when -4 is divided by -3.
We can't tell the result from +4 divided by +3.
*The formula is not enough to give you the answer;* you
should sketch the vector and adjust the answer.

Look at the picture to see that the orientation of
**-k** (expressed in degrees 0..360 counter clockwise
from the x axis) is (180° + 53.13°) = 233.13°.

What is the orientation of the vector represented by: **p** = (3,-4)^{T} ?

Use the calculator application on your computer.