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

Sep 29, 2016

(4,0) in rectangular coordinates = (4,0) in polar coordinates.

#### Explanation:

In rectangular coordinates, (x,y) represents the x and y position of the point in the plane.
In polar coordinates, it is represented by (r, $\theta$), where r is the distance from the origin and $\theta$ is the counterclockwise angle in radians.
The conversion from rectangular to polar can be achieved by the formulas:
${r}^{2} = {x}^{2} + {y}^{2}$
$\theta = \arctan \left(\frac{y}{x}\right)$

In our case, ${r}^{2} = {4}^{2} + 0$ $\implies r = 4$
And $\arctan \left(\frac{0}{4}\right) = 0 \implies \theta = 0$

So, our polar coordinates are (4,0).