# How do you convert (0,2) from cartesian to polar coordinates?

Jul 10, 2017

$\left(2 , \frac{\pi}{2}\right)$

#### Explanation:

A polar coordinate is in the form $\left(r , \theta\right)$, where $r$ is the distance from the origin and $\theta$ is the corresponding angle. We can see here that $r = 2$ and $\theta = \frac{\pi}{2}$. However, we can also use the following formulas:

${r}^{2} = {x}^{2} + {y}^{2}$

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

${r}^{2} = {x}^{2} + {y}^{2}$
$r = \sqrt{{x}^{2} + {y}^{2}}$
$r = \sqrt{{0}^{2} + {2}^{2}}$
$r = 2$

$\tan \theta = \frac{2}{0}$
This is undefined, but $\tan \left(\frac{\pi}{2}\right)$ is undefined anyways.

The polar coordinate is $\left(2 , \frac{\pi}{2}\right)$.

Jul 10, 2017

$\left(2 , \frac{\pi}{2}\right)$

#### Explanation:

$\text{to convert from "color(blue)"cartesian to polar}$

$\text{that is " (x,y)to(r,theta)" where}$

•color(white)(x)r=sqrt(x^2+y^2)

•color(white)(x)theta=tan^-1(y/x)color(white)(x);-pi< theta<= pi

$\text{here " x=0" and } y = 2$

$\Rightarrow r = \sqrt{{0}^{2} + {2}^{2}} = 2$

$\theta = {\tan}^{-} 1 \left(\frac{2}{0}\right) \leftarrow \textcolor{red}{\text{ undefined}}$

$\Rightarrow \theta = \frac{\pi}{2}$

$\Rightarrow \left(0 , 2\right) \to \left(2 , \frac{\pi}{2}\right)$