Question

How do you convert `r = 1 + 2 sin theta` to rectangular form?

Answer 1

`(x^2+y^2-2y)^2=x^2+y^2`

Explanation:

Multiply each term by `r` to get `r^2=r+2rsintheta`

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

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

`x^2+y^2-2y=sqrt(x^2+y^2)`

`(x^2+y^2-2y)^2=x^2+y^2`