Question

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

Answer 1

`(2, pi/2)`

Explanation:

A polar coordinate is in the form `(r, theta)`, where `r` is the distance from the origin and `theta` is the corresponding angle. We can see here that `r=2` and `theta=pi/2`. However, we can also use the following formulas:

`r^2=x^2+y^2`

`tan theta = y/x`

`r^2=x^2+y^2`
`r=sqrt(x^2+y^2)`
`r=sqrt(0^2+2^2)`
`r=2`

`tan theta = 2/0`
This is undefined, but `tan (pi/2)` is undefined anyways.

The polar coordinate is `(2, pi/2)`.

Answer 2

`(2,pi/2)`

Explanation:

`"to convert from "color(blue)"cartesian to polar"`

`"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`

`"here " x=0" and " y=2`

`rArrr=sqrt(0^2+2^2)=2`

`theta=tan^-1(2/0)larrcolor(red)" undefined"`

`rArrtheta=pi/2`

`rArr(0,2)to(2,pi/2)`