1. What is Coordinate Rotation?

Coordinate rotation is a transformation that changes the orientation of a point around the origin (0,0) by a specified angle while maintaining the same distance from the origin. It's fundamental in computer graphics, physics, and engineering.

2. How Does the Calculator Work?

The calculator uses the rotation formulas:

Where:

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

Explanation: The formulas preserve the distance from the origin while changing the angle by θ radians.

3. Applications of Coordinate Rotation

Details: Used in computer graphics for object transformations, in physics for changing reference frames, in robotics for manipulator kinematics, and in navigation systems.

4. Using the Calculator

Tips: Enter the original x and y coordinates (unitless values) and the rotation angle in radians (π radians = 180°). 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. For example, 90° = π/2 ≈ 1.5708 radians.

Q2: What happens when θ = 0?
A: The coordinates remain unchanged (x' = x, y' = y).

Q3: Does the rotation preserve distances?
A: Yes, the distance from origin √(x² + y²) remains the same after rotation.

Q4: What about rotation around another point?
A: First translate to origin, rotate, then translate back. This requires additional calculations.

Q5: Can I rotate 3D coordinates with this?
A: No, this is for 2D rotation only. 3D rotation requires more complex matrix operations.