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Given that we have $x=x' \cos \theta - y' \sin \theta $ and $y=x' \sin \theta +y' \cos \theta $ ,how can I express $x',y'$ in terms of $x,y$ and $a$ ?

I've browsed through the site to seek for some help but I've found that most of the questions involving rotation of coordinates involve the knowledge of matrices or vectors which I haven't yet studied.

Can you guys help me solve the problem without the use of matrices,or vectors or some other too advanced technique (for my level) ?

I've not been able to make any usefull attempt as I haven't clear in my mind how to get started.

Thanks in advance.

Mr. Y
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    Multiply the first equation by $\cos(\theta)$ and the second by $\sin(\theta)$. Then add the two equations and solve for $x'$. You can find $y'$ similarly. –  Dec 02 '15 at 16:44
  • That was pretty clever. Thank you @Bye world – Mr. Y Dec 02 '15 at 16:46

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