1. ## Cartesian formula for Archimedean Sprial please

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.

2. Originally Posted by rainer
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 $r=a+b\theta,\,a,b\in\mathbb{R}$, then by conversion to rectangular coordinates, we have $\sqrt{x^2+y^2}=a+b\tan^{-1}\left(\tfrac{y}{x}\right)$

We can't simplify this any further...