Question

Is it possible to convert arbitrary polar equation to it's cartesian? such as r=aθ (spiral)

Answer 1

\[r=\sqrt{x^2+y^2}\]

Answer 2

and how about the θ ? I tried to convert it as arctan(y/x) but it simply doesn't work

Answer 3

\[x=r\cos \theta\]\[y=r\sin \theta\]

Answer 4

why do you want to do that ? ! and
\[\theta \neq \arctan(x/y)\]

Answer 5

I'm just curious about spirals in cartesian, and maybe not at all ranges but it worked pretty well sometimes because \[x= r\cos \theta , y=r \sin\theta \\ \frac{y}{x}=\tan\theta \\ \theta=\arctan \left(\frac{y}{x} \right)\]

Answer 6

\[\theta=\arctan2(x,y)=\begin{cases} \arctan\left| \frac yx\right | & x>0 \\\arctan\left|\frac yx\right |+\pi&x<0&y\geq0 \\\arctan\left|\frac yx\right |-\pi&x<0&y<0 \\ \frac \pi2 &x=0 &y>0\\-\frac\pi2&x=0&y<0\\0&x=0&y=0\end{cases} \]

Answer 7

the verdict.. it's not always possible to convert arbitrary polar equation?

Answer 8

I think It's possible ! but It's useless !

Answer 9

so its easy if you only want a quater turn in the graph, otherwise it gets complicated