Vector Analysis 2: Sum Formulas for Cosine & Sine

[rafaelpol]

Homework Statement

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

Homework Equations

Suggestion: use the following vectors

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

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?

Thanks

 

[Office_Shredder]

Changing y to -y in B is the same thing as using C instead of B

 

[rafaelpol]

I found now what was the problem (I made a mistake while calculating the module of C). Thank you very muchl