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 fundamental in mathematics, physics, and engineering for switching between coordinate systems.

2. How Does the Calculator Work?

The calculator uses these conversion formulas:

Where:

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

Explanation: The x-coordinate is found by projecting the point onto the x-axis, while the y-coordinate is found by projecting onto the y-axis.

3. Applications of Coordinate Conversion

Details: Used in electrical engineering (phasors), physics (vector analysis), computer graphics, and navigation systems. Essential when different problems are easier solved in different coordinate systems.

4. Using the Calculator

Tips: Enter magnitude (r ≥ 0) and angle in radians. For degrees, convert first (radians = degrees × π/180). Negative angles represent clockwise rotation.

5. Frequently Asked Questions (FAQ)

Q1: Can I use degrees instead of radians?
A: The formulas require radians. Convert degrees to radians by multiplying by π/180 (≈0.0174533).

Q2: What about negative radius values?
A: While mathematically possible (point in opposite direction), physical systems typically use r ≥ 0.

Q3: How precise are the results?
A: Results are accurate to 4 decimal places. For exact values, keep π in symbolic form.

Q4: Can I convert back to polar coordinates?
A: Yes, using \( r = \sqrt{x^2 + y^2} \) and \( \theta = \arctan(y/x) \) (with quadrant adjustment).

Q5: When would I use polar vs rectangular?
A: Polar is better for circular/rotational systems; rectangular is better for grid-based systems and vector addition.