Originally Posted by

**osudude** Here is the question:

By expanding out $\displaystyle (rcos(\alpha + \theta), rsin(\alpha + \theta)) $, verify the formula:

$\displaystyle p_{\theta}(x,y) = (xcos(\theta) - ysin(\theta), xsin(\theta) + ycos(\theta)) $

Ok, now I believe that $\displaystyle x=rcos(\alpha) $ and $\displaystyle y=rsin(\alpha)$. Also, if you expand out the first formula you get

$\displaystyle (rcos(\alpha) + rcos(\theta), rsin(\alpha) + rsin(\theta)) = (x + rcos(\theta), y + rsin(\theta)) $