1. What is Rectangular to Polar Conversion?

Rectangular to polar conversion is a mathematical process that transforms Cartesian coordinates (x, y) into polar coordinates (r, θ). This is particularly useful in fields like physics, engineering, and navigation where polar coordinates often simplify problems involving circular or rotational symmetry.

2. How Does the Calculator Work?

The calculator uses the following equations:

Where:

• \( x \) — Horizontal coordinate
• \( y \) — Vertical coordinate
• \( r \) — Distance from origin (radius)
• \( \theta \) — Angle from positive x-axis

Explanation: The radius represents the straight-line distance from the origin to the point, while the angle represents the direction from the positive x-axis.

3. Importance of Polar Coordinates

Details: Polar coordinates are essential in many scientific and engineering applications, particularly when dealing with circular motion, wave propagation, or any system with radial symmetry.

4. Using the Calculator

Tips: Enter the x and y coordinates in any consistent units. The calculator will output the radius in the same units and the angle in radians (0 to 2π).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between atan and atan2?
A: atan2(y,x) is preferred as it correctly handles all quadrants and special cases (like x=0), while atan(y/x) only works for angles between -π/2 and π/2.

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

Q3: What if both x and y are zero?
A: The origin (0,0) has r=0 but an undefined angle. Our calculator handles this case specially.

Q4: Can I use negative radius values?
A: In standard polar coordinates, radius is always non-negative. Negative radii are sometimes used in specialized applications but aren't supported here.

Q5: How precise are the results?
A: Results are rounded to 4 decimal places. For exact values, consider symbolic computation software.