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Vector transformation, cylindrical to Cartesian 
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#1
Mar1112, 11:36 AM

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? 


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