arc tan( y/x ) = arc tan( 4/3 ) = arc tan( 1.333333333333 ) = 53.13^{o}

The diagram shows the vector represented by **k = (3,4) ^{T}**.
Its orientation was calculated to be 53.13

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^{o}

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 pictue to see that the orientation of
**-k** (expressed in degrees 0..360 counter clockwise
from the x axis) is (180^{o} + 53.13^{o}) = 233.13^{o}.