Vector transformation, cylindrical to Cartesian

1. Mar 11, 2012

tomwilliam

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.
P.S. Why does the latex break down when the equation is too long?

Last edited: Mar 11, 2012