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

Question

1555 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-22T13:27:05

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

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

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