1. What is Polar to Cartesian Conversion?

The polar to Cartesian conversion transforms coordinates from the polar system (r, θ) to the Cartesian system (x, y). This is fundamental in mathematics, physics, and engineering for working with different coordinate systems.

2. How Does the Calculator Work?

The calculator uses the conversion formulas:

Where:

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

Explanation: The formulas project the polar coordinates onto the x and y axes using trigonometric functions.

3. Importance of Coordinate Conversion

Details: Many physical systems are naturally described in polar coordinates (like circular motion), while Cartesian coordinates are often more practical for calculations and visualization.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What if my angle is in degrees?
A: Convert degrees to radians first (multiply by π/180). Many calculators have a degree-to-radian function.

Q2: Can the radius be negative?
A: In standard polar coordinates, radius is typically ≥ 0. Negative radii are sometimes used in extended systems.

Q3: How precise are the results?
A: Results are accurate to 4 decimal places. For higher precision, use more advanced computational tools.

Q4: What are common applications?
A: Used in physics (circular motion), engineering (signal processing), computer graphics, and navigation systems.

Q5: How does this relate to complex numbers?
A: Polar form is often used to represent complex numbers, with Euler's formula connecting the two representations.