Rotation of axes in two dimensions

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a rotation of axes in two dimensions is a <a href="/facts/Map_(mathematics)/FABF1l2f">mapping</a> from an xy-<a href="/facts/Cartesian_coordinate_system/lkTqvMmB">Cartesian coordinate system</a> to an x′y′-Cartesian coordinate system in which the <a href="/facts/Origin_(mathematics)/Lm26tRCB">origin</a> is kept fixed and the x′ and y′ axes are obtained by rotating the x and y axes <a href="/facts/Clockwise/3Npe4Swe">counterclockwise</a> through an angle 
 
 
 
 θ
 
 
 {\displaystyle \theta }
 
. A point P has coordinates (x, y) with respect to the original system and coordinates (x′, y′) with respect to the new system. In the new coordinate system, the point P will appear to have been rotated in the opposite direction, that is, clockwise through the angle 
 
 
 
 θ
 
 
 {\displaystyle \theta }
 
. A rotation of axes in more than two dimensions is defined similarly. A rotation of axes is a <a href="/facts/Linear_map/Q1PBKNVV">linear map</a> and a <a href="/facts/Rigid_transformation/0KzWYQXl">rigid transformation</a>.

Rotation of axes in two dimensions open-in-new

Rotation of axes in two dimensions