Expressing parametric equations of a spiral in terms of X coordinate

Question

I'd like to draw the spiral as a bitmap graphics.

Given a simplified parametric form of an Archimedean spiral for x and y as functions of t:

x(t) = t * sin(t)
y(t) = t * cos(t)

How can I derive y as function of x (y(x))? Is that possible and what would be the steps?

Thank you.

Answer 1

Well, $x^2+y^2=t^2$, and $x/y=\tan(t)$, so perhaps you could do $x^2+y^2=\left(\text{Tan}^{-1}(x/y)\right)^2$.

Although there would probably be some issues with the domain this works on, and how to convert this into the form $y=f(x)$. But hopefully this is a start to get it into cartesian form.