how to write floor function vectors in polar coordinates

Question

let $$\lfloor{x}\rfloor=y$$ And $$z=x-\lfloor{x}\rfloor$$ Plot the following vector in polar coordinates:

$$x\hat{\imath}+(y/z)\hat{\jmath}$$ I know that while transforming from cartesian to polar we substitute$$ x=r\sin{\theta}$$ and $$y=rcos{\theta}$$ But here the floor function and the vector form in polar coordinate pose sufficient difficulty for me to proceed.Please help.

Answer 1

You can't simplify it at all, $\lfloor{x}\rfloor=\lfloor{r\cos(\theta)}\rfloor$ in polar coordinates. Just substitute for $x=r\cos(\theta)$ and $y=r\sin(\theta)$ to get your answer.