Question

How do you convert `r = 6sinθ` into rectangular form?

Answer 1

`x^2+y^2-6y=0`

Explanation:

The relation between polar coordinates `(r,theta)` and rectangular coordinates `(x,y)` are given by `x=rcosthata` and `y=rsintheta` and hence `r=sqrt(x^2+y^2)`

Hence `r=6sintheta` is nothing but

`rxxr=6sinthetaxxr` or

`r^2=6rsintheta` or

`x^2+y^2=6y` or

`x^2+y^2-6y=0`

graph{x^2+y^2-6y=0 [-10, 10, -2.32, 7.68]}