So when I am working on homework and I am asked to find the direction angle of a vector I usually to the inverse of tan(y/x). Whatever answer I get, I usually add or subtract from the answer 180 or 360 to get the direction angle. However, I do not know which one to do in which situation.
For example, on one of my problems it was <-10, 9>. I took the inverse of tan(9/-10) and added 360° to the result for an answer of 138.01°.
Another example, <-6,0>,I took the inverse of tan(0/-6) and added 180° for an answer of 0°.
I'm just not sure when exactly to do which. I got the answer correct because I had an answer sheet to check my work, but if I didn't get the answer right the first time I would try something else. That won't work on my exam when I don't have an answer sheet to check my homework.