Mathematics-Online lexicon: Rotation of a Cartesian Coordinate System

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	Mathematics-Online lexicon:
	Rotation of a Cartesian Coordinate System

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Rotating the

-plane by the angle $\alpha$ about the

-axis the coordinates of a point

transform as follows:

$\displaystyle x' = \cos(\alpha)\,x\, + \,\sin(\alpha)\,y,\quad y' = -\sin(\alpha)\,x\, + \,\cos(\alpha)\,y,\quad z' = z\, .$

$\includegraphics[width=0.7\textwidth]{rotation}$

Analogous formulas are obtained by rotations about the - and the -plane.

Example:

automatically generated 3/28/2008