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

Aug 4, 2018

$\text{ }$
Polar form: color(red)((r,theta)=(+-2, pi)

#### Explanation:

$\text{ }$
Given:

Cartesian coordinates: color(blue)((-2,0)

How do we convert from Cartesian coordinates to Polar form?

Polar Form: color(blue)((r, theta)

Examine the sketch below:

Important formula to remember:

color(blue)(x^2+y^2=r^2

color(blue)(tan(theta)=y/x

color(blue)(cos(theta)=x/r rArr x = r cos(theta)

color(blue)(sin(theta)=y/r rArr y = r sin(theta)

Let us identify the point on the Cartesian Plane:

Cartesian coordinates: color(blue)((-2,0)

Note that the angle is $\pi$

Hence color(red)(theta = pi

Use the formula: color(blue)(x^2+y^2=r^2

$\Rightarrow {\left(- 2\right)}^{2} + {\left(0\right)}^{2} = {r}^{2}$

Swap sides:

$\Rightarrow {r}^{2} = {\left(- 2\right)}^{2} + {\left(0\right)}^{2}$

$\Rightarrow {r}^{2} = 4 + 0$

$\Rightarrow {r}^{2} = 4$

Taking the color(red)(sqrt on both sides:

$\Rightarrow \sqrt{{r}^{2}} = \sqrt{4}$

$\Rightarrow r = \pm \sqrt{4}$

$\Rightarrow r = \pm 2$

Hence, the required Polar form: color(red)((+-2, pi)

Hope this helps.