Rotação de Vetor 2D

The 2D Vector Rotation Calculator rotates a two-dimensional vector (x, y) by an angle θ (in degrees or radians) in the Cartesian plane. The operation uses a 2D rotation matrix, which transforms the original vector coordinates into new coordinates after rotation around the origin (0,0). The result is a new vector with the same magnitude but changed orientation.

The calculation is based on the formula: x' = x·cos(θ) - y·sin(θ) and y' = x·sin(θ) + y·cos(θ). These equations derive from multiplying the rotation matrix R(θ) by the column vector [x; y]. The tool accepts input in degrees or radians, automatically converts if needed, and displays the resulting vector with precision.

This calculator is useful in various fields such as computer graphics (rotating objects, sprites), physics (circular motion, forces), robotics (orienting robotic arms), and analytic geometry. For example, when programming a game, you can rotate a character's position around the origin. It is also applied in particle simulations and image processing.

Important precautions: rotation is always around the origin (0,0). To rotate around an arbitrary point, you must translate the vector to the origin, apply the rotation, and then translate back. Also, ensure you use the correct angle unit (degrees or radians) to avoid errors. The calculator assumes angles are measured counterclockwise.