Question

How do you convert `r csc theta = 8` to rectangular form?

Answer 1

`x^2+y^2-8y=0`

Explanation:

Relation between polar form `(r,theta)` and rectangular form `(x,y)` is given by

`rcostheta=x`, `rsintheta=y`, `r^2=a^2+b^2` and `tantheta=b/a`

Hence `rcsctheta=8` can be written as

`r/sintheta=8` or

`r^2/(rsintheta)=8` or

`(x^2+y^2)/y=8` or `x^2+y^2=8y` or

`x^2+y^2-8y=0`

This is the equation of a circle.

graph{x^2+y^2-8y=0 [-20, 20, -10, 10]}