How do you graph $r=sqrt(cos(2*theta))$ ?

Question

16512 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-01T07:59:21

Hence it is in polar coordinates we have that

$x=r*cos(theta)$ and $y=r*sin(theta)$

so we have that $r^2=(x^2+y^2)$

and

$cos(2theta)=cos^2theta-sin^2theta=(x/r)^2-(y/r)^2$

From our given relation we have that

$r=sqrt(cos(2theta))=>r^2=cos(2theta)=> r^2=(1/r^2)(x^2-y^2)=>r^4=(x^2-y^2)=> (x^2+y^2)^2=x^2-y^2$

The graph of $(x^2+y^2)^2=x^2-y^2$ is

enter image source here

How do you graph r=sqrt(cos(2*theta))r=sqrt(cos(2*theta))?