# How do you convert (0, −4)  into polar form?

Oct 26, 2016

The polar coordinates are $\left(4 , \frac{3 \pi}{2}\right)$

#### Explanation:

Use the definition
$x = r \cos \theta$
$y = r \sin \theta$
${x}^{2} + {y}^{2} = {r}^{2}$

$\tan \theta = \frac{y}{x}$

where $\left(x , y\right)$are the cartesian coordinates
and $\left(r , \theta\right)$are the polar coordinates
Here we have $\tan \theta = - \frac{4}{0} = - \infty$
So $\theta = \frac{3 \pi}{2}$
and ${r}^{2} = 0 + 16$ $\implies$ $r = 4$
So the polar coordinates are $\left(4 , \frac{3 \pi}{2}\right)$