CALCULATOR
2D Rotation about Origin Component Calculator
2D Rotation about Origin Component. Coordinate: 0=x, 1=y: x coordinate, y coordinate only. Example: X: 3 m, Y: 4 m, Angle: 90 degrees, Coordinate: 0=x, 1=y: 0 number gives -4 m. Real bounded inputs with supplied units; numerical selected result only. Original useful product scope; historical catalog title does not grant missing modes or source parity.
Real bounded inputs with supplied units; numerical selected result only. Original useful product scope; historical catalog title does not grant missing modes or source parity. Derivation: Apply orthogonal planar rotation matrix; positive angles counterclockwise.
Accepted inputs: X: -1,000 to 1,000 m; Y: -1,000 to 1,000 m; Angle: -180 to 180 degrees; Coordinate: 0=x, 1=y: choose x coordinate (0), y coordinate (1).
How the calculation works
x′=x cosθ-y sinθ; y′=x sinθ+y cosθ
Worked example
With x 3 m, y 4 m, angle 90 degrees, coordinate: 0=x, 1=y x coordinate, 2d rotation about origin component is -4 m.
Assumptions and limits
Real bounded inputs with supplied units; numerical selected result only. Original useful product scope; historical catalog title does not grant missing modes or source parity. Derivation: Apply orthogonal planar rotation matrix; positive angles counterclockwise.