# Vector transformation, cylindrical to Cartesian

by tomwilliam
Tags: cartesian, cylindrical, transformation, vector
 P: 128 1. The problem statement, all variables and given/known data I have a result which is in the form (cylindrical coordinates): $$A\boldsymbol{e_{\theta }}=kr\boldsymbol{e_{\theta }}$$ And I have to provide the answer in cartesian coordinates. 2. Relevant equations I know that the unit vectors: $$\boldsymbol{\hat{\theta} }=\begin{bmatrix}-sin\ \theta \\ cos\ \theta \end{bmatrix}$$ and that $$r=\sqrt{x^{2}+y^{2}}$$ 3. The attempt at a solution $$kr\boldsymbol{e_{\theta }} =k\left (\sqrt{x^{2}+y^{2}}\right )$$ $$\left (-sin\left(tan^{-1}\left(\frac{y}{x}\right )$$ $$\right )\boldsymbol{e_{x}}$$ $$+cos\left (tan^{-1}\left (\frac{y}{x}\right )\boldsymbol{e_{y}} \right )\\$$ I can't seem to get further than this. I don't know if I've made a mistake, or whether there is some trig identity that can help me simplify further, but I know the final answer and it is much simpler. Any help much appreciated. Thanks in advance P.S. Why does the latex break down when the equation is too long?