The formula for graphing an Archimedean spiral is always given in polar coordinates. I need to know the formula in Cartesian coordinates (x,y). Can anyone help? Thanks.
The formula for graphing an Archimedean spiral is always given in polar coordinates. I need to know the formula in Cartesian coordinates (x,y). Can anyone help? Thanks.
It's an implicit equation that you can't solve for y.
So if $\displaystyle r=a+b\theta,\,a,b\in\mathbb{R}$, then by conversion to rectangular coordinates, we have $\displaystyle \sqrt{x^2+y^2}=a+b\tan^{-1}\left(\tfrac{y}{x}\right)$
We can't simplify this any further...
Last edited by Chris L T521; Sep 7th 2009 at 03:41 PM.
Reason: used wrong spiral equation... ><