Question

How do you solve `x^4-2x^2+2=0` in polar form?

Answer 1

`r^4cos^4theta-2r^2cos^2theta+2=0`

Explanation:

The relation between polar coordinates `(r,theta)` and rectangular Cartesian coordinates `(x,y)` are given by

`x=rcostheta` and `y=rsintheta` or `r^2=x^2+y^2`

Hence `x^4-2x^2+2=0` can be written as

`r^4cos^4theta-2r^2cos^2theta+2=0`

or `r^4cos^4theta-2r^2cos^2theta+2=0`