3-8 ■ Rotation of Axes Determine the XY-coordinates of the given point if the coordinate axes are rotated through the indicated angle
The XY-coordinates of the given point and the coordinate axes are rotated through at .
The XY-coordinates of the given point is and the coordinate axes are rotated through at angle .
The -axes and y-axes in a coordinate plane are rotated through the acute angle to produce the -axis and -axis. Then, the coordinates and of a point in the and the -planes are
Here, is the coordinates of the point and is the angle at which coordinate axis are rotated.
Substitute for , for and for in equation (1).
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