Unleash Rotations in 2D Space!
Visualize and calculate 2D Rotation Matrices with ease. Enter an angle, choose your units, and watch the magic happen!
Enter Rotation Angle
Define the angle and units to calculate the rotation matrix.
Rotation Matrix Formula:
Resultant Rotation Matrix:
Visual Representation:
Observe how the vector (gray) rotates to a new position (blue) based on the calculated matrix.
Understanding 2D Rotation Matrices
A 2D rotation matrix is a transformation matrix that rotates a vector in a two-dimensional plane. It's defined by a single angle, θ, and is crucial in various fields like computer graphics, physics, and engineering.
- Formula: The standard rotation matrix is given by:
- Degrees vs Radians: Angles can be specified in degrees or radians. Radians are the standard unit in mathematics, where 360 degrees equals 2π radians.
- Applications: Rotation matrices are used to rotate images, perform coordinate transformations, and analyze rotational motion.
- Further Learning: Explore linear algebra textbooks or online resources like Khan Academy for a deeper understanding of matrices and transformations.