For the sake of simplicity, I will ask the question in 2D:
Why is the arccos of a negative number (between -1 and 0, not including 0) an obtuse angle measured from the +X axis by definition, and not an acute angle measured from the -X axis?
I understand how to show empirically why it is true, using the unit circle to first find the angle between the vector and the -x axis, then taking 180-angle.
But, when I try to show it through a simple drawing, I get confused.
In Image 1, I have the vector from the origin pointing to (5,5), and the angle I calculate is 45 degrees using the given equation. Using the same equation in Image 2, the equation yields a value of 135 degrees, but the drawing seems to suggest that I am finding said angle using the cosine of -5/sqrt(50), which would make it the angle between the vector and the -x axis the one that I am calculating, not the angle between the vector and the +x axis. Perhaps I am not explaining my confusion well enough, but I hope it comes through.