Thread: Polar coordinates to Cartesian coordinates

1. Polar coordinates to Cartesian coordinates

Convert the system in the polar coordinates r'=(1-r), theta' =sin(theta/2)^2 into cartesian coordinates.

2. Re: Polar coordinates to Cartesian coordinates

Hey nm321.

Can you show us your attempts?

4. Re: Polar coordinates to Cartesian coordinates

This is all I have so far. I'm stuck

5. Re: Polar coordinates to Cartesian coordinates

You have a linear transformation from one polar coordinate system to another: $r'= 1- r$ and $\theta'= sin^2(\theta/2)$. I would start by using the "half angle formula":
$sin(\theta/2)= \sqrt{(1/2)(1- cos(\theta)}$ so that $\theta'= sin^2(\theta/2)= \frac{1}{2}(1- cos(\theta)$. Now use the fact that $\theta= arctan\left(\frac{y}{x}\right)$, $r= \sqrt{x^2+ y^2}$, $\theta'= arctan\left(\frac{y'}{x'}\right)$, and $r'= \sqrt{x'^2+ y'^2}$