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Math Help - Transpose problem

  1. #1
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    Aug 2009
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    Transpose problem

    Hi guys,

    I'm having a problem with transposing the equation below to make Vf the subject:

    D = | Pf + i1f*Rf*cos(Vf) + i2f*Rf*sin(Vf) - P2 |

    | | denotes the length of the vector as in sqrt(x^2 + y^2 + z^2)

    I know the trig identity where a*cos(x) + b*sin(x) is equal to R*cos(x - alpha) where R = sqrt(a^2 + b^2) and alpha = atan(b/a) which would get rid of the two instances of Vf.

    However Pf, i1f, i2f, and P2 are all 3D vectors which is where I'm having the problem. I can't see how I can transpose the equation to make Vf the subject. Is there another identity I'm missing?

    Any help is much appreciated.
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  2. #2
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    Aug 2009
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    Hey guys,

    I've tried expanding the equation out using the Rcos(x - alpha) identity but still end up with 3 instances of x on that side of the equation for each component of the x, y, z vector. I'm really stuck here. No matter which way I look at it I can't seem to isolate X. I've tried using different identities but can't solve it. The original equation works when I substitute known data so it must be able to be transposed but I can't see it at the moment. Can somebody help?
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  3. #3
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    Anybody? I'm really stuck here
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