1. What is Polar to Rectangular Conversion?

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

2. How Does the Calculator Work?

The calculator uses the conversion equations:

Where:

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

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

3. Importance of Coordinate Conversion

Details: Converting between coordinate systems is crucial in fields like physics (for vector analysis), engineering (for signal processing), and computer graphics (for rendering).

4. Using the Calculator

Tips: Enter the radius (must be ≥ 0) and angle in radians. For degrees, convert to radians first (multiply by π/180). The calculator will output the corresponding x and y coordinates.

5. Frequently Asked Questions (FAQ)

Q1: What if my angle is in degrees?
A: Convert degrees to radians first by multiplying by π/180 (≈0.0174533). Many calculators have a degree-to-radian conversion function.

Q2: Can r be negative?
A: In standard polar coordinates, r should be ≥0. Negative r values would represent the point in the opposite direction (θ+π).

Q3: What's the range for θ?
A: θ can be any real number, but typically we use 0 ≤ θ < 2π or -π < θ ≤ π for principal values.

Q4: How precise are the results?
A: Results are rounded to 4 decimal places. For higher precision, use a scientific calculator or computer algebra system.

Q5: What are common applications?
A: Used in antenna radiation patterns, orbital mechanics, complex numbers, and any system with radial symmetry.