When you rotate passivly an arbitrary vector in [tex]P[/tex] (which is not in the origin of a coordinate system), you will get the following new coordinates for the same vector:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]x'=x \cos\theta+y\sin \theta[/tex]

[tex]y'=\frac{1}{r}(y\cos \theta-x\sin\theta)[/tex]

where [tex]r[/tex] is the distance from the origin to the point [tex]P[/tex] and [tex]x,y[/tex] are the components of the vector. Can somebody explain me, why you have to divide by [tex]r [/tex] in the second equation?

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# Passive Rotation

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