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Math Help - Expansion of a rotation-formula

  1. #1
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    Expansion of a rotation-formula

    Here is the question:

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

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


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

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

    but from here I am stuck. Am I onto something here or am I going at this all wrong? thanks.
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  2. #2
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    Quote Originally Posted by osudude View Post
    Here is the question:

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

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


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

     (rcos(\alpha) + rcos(\theta), rsin(\alpha) + rsin(\theta)) = (x + rcos(\theta), y + rsin(\theta))
    No, you don't. cos(\alpha+ \theta) is NOT equal to cos(\alpha)+ cos(\theta), it is equal to cos(\alpha)cos(\theta)- sin(\alpha)sin(\theta).

    but from here I am stuck. Am I onto something here or am I going at this all wrong? thanks.
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