1. What is Graph Rotation?

Graph rotation is a transformation that turns every point of a figure through a specified angle about a fixed point (usually the origin). It preserves the shape and size of the figure while changing its orientation.

2. How Does the Rotation Matrix Work?

The calculator uses the standard 2D rotation matrix:

Where:

• \( (x, y) \) — Original coordinates
• \( (x', y') \) — Rotated coordinates
• \( \theta \) — Rotation angle in radians
• \( \cos\theta \) — Cosine of the angle
• \( \sin\theta \) — Sine of the angle

Explanation: The matrix multiplication transforms the original coordinates to new positions while maintaining the same distance from the origin.

3. Importance of Rotation Calculation

Details: Rotation calculations are fundamental in computer graphics, robotics, physics simulations, and engineering applications where coordinate transformations are needed.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: How do I convert degrees to radians?
A: Multiply degrees by π/180 (approximately 0.0174533). Many calculators have a degree-to-radian conversion function.

Q2: What's the difference between clockwise and counter-clockwise rotation?
A: Counter-clockwise rotation uses positive angles in the standard rotation matrix. For clockwise rotation, use negative angles.

Q3: Can I rotate about a point other than the origin?
A: Yes, but you need to first translate the point to the origin, rotate, then translate back.

Q4: Does rotation preserve distances?
A: Yes, rotation is a rigid transformation that preserves distances between points and angles between lines.

Q5: How is this used in real-world applications?
A: Applications include computer graphics animation, satellite positioning, robotic arm movements, and 3D modeling.