1. What is Polar to Cartesian Conversion?

Polar to Cartesian conversion is a mathematical process that transforms coordinates from the polar system (r, θ) to the Cartesian system (x, y). This is essential in many fields including physics, engineering, and computer graphics.

2. How Does the Calculator Work?

The calculator uses the following conversion formulas:

Where:

• \( r \) — Radius (distance from origin)
• \( \theta \) — Angle in radians (measured from positive x-axis)
• \( x \) — Horizontal coordinate
• \( y \) — Vertical coordinate

Explanation: The formulas use trigonometric functions to project the polar coordinates onto the Cartesian plane.

3. Importance of Coordinate Conversion

Details: Converting between coordinate systems is crucial for solving problems in different contexts. Many physical systems are naturally described in polar coordinates but need Cartesian coordinates for analysis or visualization.

4. Using the Calculator

Tips: Enter the radius (must be ≥ 0) and angle in radians. The calculator will compute the corresponding x and y Cartesian coordinates.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between polar and Cartesian coordinates?
A: Polar uses (r,θ) - distance and angle, while Cartesian uses (x,y) - horizontal and vertical positions.

Q2: How do I convert degrees to radians?
A: Multiply degrees by π/180. Many calculators have a degree-to-radian conversion function.

Q3: Can r be negative in polar coordinates?
A: Mathematically yes, but this calculator assumes r ≥ 0 as negative radii can be represented by adding π to θ.

Q4: What are common applications of polar coordinates?
A: Used in navigation, antenna radiation patterns, circular motion analysis, and any system with radial symmetry.

Q5: How precise are the results?
A: Results are accurate to 4 decimal places, sufficient for most practical applications.