Coordinate transformation under rotation

AI Thread Summary
The discussion focuses on the mathematical derivation of coordinate transformations when a system is rotated around the Z-axis. The new coordinates are expressed as X' = xcos(θ) - Ysin(θ), Y' = Xsin(θ) + Ycos(θ), and Z' = Z, where θ is the angle of rotation. Participants are encouraged to refer to rotation matrices for a clearer understanding of how these transformations are derived. The conversation emphasizes the need to understand the rotation of basis vectors to grasp the underlying mathematics. A deeper exploration of rotation matrices is suggested for further clarity.
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If a system is rotated around Z axis then the new coordinates are X'= xcos() - Y sin(),

Y'= Xsin() + Ycos()

Z'= Z

How is this obtained ??

() --->theta , angle of rotation around Z axis .
 
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Simply look at rotating the basis vectors through an angle theta about the z-axis.
 
i am nt getting it , need to know the mathematical derivation
 
how to get that rotation matrix ??
 

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