Question

How do you convert `r=2(cos(theta))^2` into cartesian form?

Answer 1

It is `(x^2+y^2)^(3/2)=2x^2`

Explanation:

Hence `x=r*costheta` and `y=r*sintheta` we have that

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

so

#r=2*(costheta)^2=>sqrt(x^2+y^2)=2*(x/r)^2=> r^2*(sqrt(x^2+y^2))=2x^2=> (x^2+y^2)^(3/2)=2x^2#