How do you convert $r^2 theta=1$ into cartesian form?

Question

3840 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-01T05:37:25

$y=x tan(1/(x^2+y^2))$ , representing a spiral from the origin that turns forever, to reach the origin..

As $r^2>0$ , its reciprocal $theta > 0$

Using the conversion formula #r(cos theta, sin theta) = (x, y),

$theta=tan^(-1)(y/x)=1/(x^2+y^2) to y = x tan (1/(x^2+y^2))$ .

I want variation of $theta in (0, oo)$ .

The graph is a spiral that approaches origin only in the limit,

as $x, y to oo$ .. .

.

How do you convert r^2 theta=1r^2 theta=1 into cartesian form?