What is a two term tangent and how am I supposed to calculate it?

[F14]

Homework Statement

determine the magnitude and direction of V

Relevant Equations

Please refer to the pictures

So, I was able to run some numbers and get a magnitude with what looks to be the distance formula. I was able to do that by first adding the (i) and(j) components from the two vectors and then taking the sums and running them through that distance formula. So far so good, but now I have to figure out the degrees of its angle.

I looked up the problem on Chegg study to see what others have done and that is when I noticed that this "atan2" process was being used to calculate the direction. I have never heard of a two-term tangent before and when I looked that up, I mostly just got references to Fortran and MatLab usage. In the solution, it states that it is -166.51 degrees. I could not replicate that answer when I tried to do it on my own. I tried inverse tan to get my degrees, but those figures were under 80 degrees and in the positive since the slope is positive.

Could I get some insight into this, please?

 

[haruspex]

never heard of a two-term tangent before

The trouble with atan(y/x) is that it loses sign information in the x and y values. If both are positive then the angle is in the first quadrant, but if both negative it is 180 degrees around in the third quadrant. Providing x and y as separate parameters solves this.

 

[fresh_42]

Your pictures are very hard to read. Neither the problem statement nor your own calculations can be clearly seen without further editing: downloads, change of brightness, zooming etc.

Please type in both: problem statement + what you did by using LaTeX. Here you can find how it is done:
https://www.physicsforums.com/help/latexhelp/