Question

How do you convert `r = 3` into rectangular form?

Answer 1

I found: `x^2+y^2=9`

Explanation:

Consider the following diagram:

We can see that the relationships between rectangular and polar coordinates are:
`r=sqrt(x^2+y^2)`
`theta=arctan(y/x)`
and:
`x=rcos(theta)`
`y=rsin(theta)`

Given our expression:
`r=3`
using our relationships of conversion.
`sqrt(x^2+y^2)=3`
square both sides:
`x^2+y^2=9`

which is a circle centred in the origin and with radius of `sqrt(9)=3`.