(adsbygoogle = window.adsbygoogle || []).push({}); 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?

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# Vector transformation, cylindrical to Cartesian

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