# Math Help - Just a quick clarification for polar coordinates.

1. ## Just a quick clarification for polar coordinates.

We have to convert from rectangular to polar coordinates.

In the first example in the book, the point to convert is (2,3)

We get r=sqrt(13) and theta=tan^(-1) (3/2), making the point (3.6, .98) I get that.

But then the next point is (4,-7), we get r=sqrt(65) and theta=tan^(-1)(-7/4)=2pi-1.05, and they give the point as (8.1,5.2). My question is, could I just put it as (8.1,-1.05) or do you need to put 2pi-1.05?

2. This is the professional way to do this problem.
$\theta=\arg (x,y) = \left\{ {\begin{array}{rc}
{\arctan \left( {y/x} \right),} & {x > 0} \\
{\arctan \left( {y/x} \right) + \pi ,} & {x < 0 \wedge y > 0} \\
{\arctan \left( {y/x} \right) - \pi ,} & {x < 0 \wedge y < 0} \\ \end{array} } \right.$