Quick Phasor Angle Question

Hello!

My question, I believe, is relatively simple to answer. I am converting an answer from rectangular form to polar form, but have the opposite sign from the answer key.
My rectangular form is : -0.52 - j160.19 .. but when I convert to polar form I get 160.2 < 89.9 (deg) ... the answer key has <-89.9 (deg).
Does this have something to do with when I take the inverse tangent of (-160.19 / -0.52) and its being in the third quadrant?

Again, I feel like I'm missing a very minor thing. Thanks in advance!

Hey Bubbleboy78.

The angle will be arctan(y/x) but it will be in the third quadrant (since both are negative) so you will need to add pi to the result to get the angle in that quadrant.

Your answer given is wrong and using R I get:

> (atan(160.19/0.52) + pi)*(180/pi)
[1] 269.814

or 269.814 degrees counter-clockwise from the real axis, which is in the third quadrant.

Ahh ok, thanks. It makes sense now... the angle I get is in the first quadrant, but I need to be in the third, so I add pi. So either 269.814 (counter clockwise) or -90.186 (clockwise).