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Vector analysis 2

  1. Jun 6, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the sum formulas for cosine and sine using vector methods.

    2. Relevant equations

    Suggestion: use the following vectors

    A= cos xi + sin xj
    B= cos yi + sin yj
    C= cos yi - sin yj

    3. The attempt at a solution

    I actually solved the question by doing the dot product of A and B and finding the cosAB = cos (x-y). Then, I changed y to -y and obtained the other formula concerning the sum of cosines. The same thing was done with the cross product of A and B in order to obtain the formulas for sum and subtraction of sines. I am not completely satisfied with this solution, since the author gives the suggestion to use a vector C. I tried doing the dot product of A and C in order to obtain cos (x+y), but it did not work out since the length of vector C is cos(2y). Same thing happened when I did their cross product to obtain sin (x+y). I am thinking I am making some kind of geometrical mistake, but I have not found what would that be. Can anyone help me on this?

  2. jcsd
  3. Jun 6, 2010 #2


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    Staff Emeritus
    Science Advisor
    Gold Member

    Changing y to -y in B is the same thing as using C instead of B
  4. Jun 6, 2010 #3
    I found now what was the problem (I made a mistake while calculating the module of C). Thank you very muchl
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