# How do you convert (-4,-4) into polar form?

Mar 10, 2018

(4sqrt2, 225°)

#### Explanation:

To convert between polar and rectangular, these formulas will help you out. (Link to the webpage I got the image from is in gray.)

So we can see that where the Cartesian/rectangular ordered pairs follow the $\left(x , y\right)$ format, polar ordered pairs follow $\left(r , \theta\right)$.

The steps here can vary, depending on whether you want to find $\theta$ or $r$ first, but we'll just find $\theta$ first for this answer.

$\tan \theta = \frac{- 4}{-} 4 = 1$
arctan(1) = 45°

We should note, however, that since $x$ and $y$ are both negative, our point is in quadrant $I I I$. 45° is just the reference angle. $\theta$ is actually 225°.

We can use one of the left-hand formulas to find $r$ now.

-4 = rcos225°

$- 4 = r \left(\frac{- \sqrt{2}}{2}\right)$

$r = - 4 \cdot \frac{2}{- \sqrt{2}} = \frac{- 8}{- \sqrt{2}} = \frac{- {\sqrt{2}}^{6}}{- \sqrt{2}} = {\sqrt{2}}^{5} = 4 \sqrt{2}$

So we have found our answer: $\left(- 4 , - 4\right)$ in polar form is (4sqrt2, 225°).

Of course, the way you write your answer is going to depend on whether they want $\theta$ in radians or degrees and whether they want you to be exact with $r$ or round, but you get the gist, hopefully.