I am trying to convert circle equation from Cartesian to polar coordinates. I know the solution is all over the Internet but what I am looking for is the exact procedure and explanation, not just the solution. If we start off with:
$(x-a)^{2} + (y-b)^{2} = r^{2}$
and use
$x=r\cos{\theta}$
$y=r\sin{\theta}$
I got something that doesn't make a lot of sense. Thanks!
Best Answer
The parametrization would be $x=r\cos\theta+a$, $y=r\sin\theta+b$. Since then $(x-a)^2+(y-b)^2=r^2\cos^2\theta+r^2\sin^2\theta=r^2$
We take $x=r\cos\theta+a$, $y=r\sin\theta+b$, instead of $x=r\sin\theta+a$, $y=r\cos\theta+b$, as it produces a circle that is oriented anticlockwise.