Question

How do you convert (5, 0) into polar coordinates?

Answer 1

`(5,0)`

Explanation:

Cartesian coordinates are represented as the ordered pair, `(x, y)`, and can be converted to polar coordinates, represented as `(r, theta)`, using the following three identities.

`x=rcos(theta)`
`y=rsin(theta)`
`r=sqrt(x^2 + y^2)`

Lets start by finding `r`. Plugging `x` and `y` into the identity for `r` yields;

`r = sqrt(5^2 + 0^2) = sqrt(5^2) = 5`

If we plug `x` and `r` into the first identity, we get;

`5 = 5cos(theta)`

`5/5 = cos(theta)`

`1= cos(theta)`

On the unit circle, `cos(0) = 1`, so `theta = 0`. Our ordered pair is therefore;

`(r, theta) = (5, 0)`