1. What is Point Rotation?

Point rotation is a transformation that moves points around a fixed center (origin) by a specified angle. It preserves distances and angles between points, making it a rigid transformation.

2. How Does the Rotation Calculator Work?

The calculator uses the rotation transformation formula:

Where:

• \( (x, y) \) — Original coordinates
• \( (x', y') \) — Rotated coordinates
• \( \theta \) — Rotation angle in radians

Explanation: The formula uses trigonometric functions to calculate the new position of a point after rotation about the origin.

3. Applications of Rotation

Details: Rotation transformations are fundamental in computer graphics, robotics, physics simulations, and geometric calculations.

4. Using the Calculator

Tips: Enter the original (x,y) coordinates and rotation angle in radians. Positive angles rotate counter-clockwise, negative angles rotate clockwise.

5. Frequently Asked Questions (FAQ)

Q1: How do I convert degrees to radians?
A: Multiply degrees by π/180. For example, 90° = π/2 ≈ 1.5708 radians.

Q2: What's the difference between rotation and revolution?
A: Rotation is turning around an internal axis (like this calculator does), while revolution is moving around an external point.

Q3: Can I rotate around a point other than the origin?
A: First translate the point to the origin, rotate, then translate back.

Q4: What are rotation matrices?
A: The rotation formulas can be represented as matrix multiplication for efficient computation.

Q5: How is this used in real-world applications?
A: Used in video games (character movement), CAD software, satellite positioning, and more.