Question

How do you convert `r*(csctheta) = sqrt(11)` into rectangular form?

Answer 1

`x^2+y^2-sqrt11y=0`

Explanation:

To convert `r*cscθ=sqrt11` into rectangular form `(x,y)`, we should use the relation between `(x,y)` and `(r,theta)`, which are

`r^2=x^2+y^2` and `rcostheta=x` and `rsintheta=y`
Note that `csctheta=1/sintheta=r/y`.

Hence `r*cscθ=sqrt11` can be written as

`r*r/y=sqrt11` or `r^2=sqrt11*y`

`x^2+y^2-sqrt11y=0`