Decode a Rotation Matrix

Decode Rotation Matrix

Enter the elements of the 2×2 rotation matrix:

Introduction:

Decode a Rotation Matrix tool allows you to input the elements of a 2×2 rotation matrix and deciphers the angle of rotation it represents.

Matrix Input:

You can input the elements of the rotation matrix in the provided table. The default values represent the identity matrix, which indicates no rotation.
Each cell in the table corresponds to an element of the rotation matrix.

Decode Rotation Matrix:

Clicking the “Decode Rotation Matrix” button calculates the angle of rotation based on the provided matrix elements.
The calculated angle of rotation is displayed below the button.

Benefits of Using This Tool:

Quick Deciphering: Easily determine the angle of rotation encoded in a given 2×2 rotation matrix.
Accuracy: Precisely calculates the angle of rotation using the matrix elements.
Educational: Helps understand the relationship between rotation matrices and angles of rotation.

FAQ:

Q: What is a rotation matrix? A: A rotation matrix is a square matrix used to perform rotations in the plane. It represents a transformation that rotates points in the plane around the origin.

Q: How does the tool calculate the angle of rotation? A: The tool uses the elements of the rotation matrix to calculate the angle of rotation using trigonometric functions.

Q: What does the identity matrix represent in terms of rotation? A: The identity matrix represents no rotation. The default values in the input table correspond to the identity matrix.