1. What is Cartesian to Polar Conversion?

Cartesian to polar conversion transforms coordinates from the rectangular (x,y) system to the polar (r,θ) system. This is useful in many fields including physics, engineering, and navigation where polar coordinates better describe circular or rotational systems.

2. How Does the Calculator Work?

The calculator uses the following formulas:

Where:

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

Explanation: The radius (r) is calculated using the Pythagorean theorem, while the angle (θ) is calculated using the arctangent function (atan2 in practice to handle all quadrants correctly).

3. Importance of Coordinate Conversion

Details: Polar coordinates are essential when dealing with circular motion, periodic functions, or any system where angles and distances from a central point are more relevant than horizontal/vertical positions.

4. Using the Calculator

Tips: Enter the x and y coordinates of your point. The calculator will provide the equivalent polar coordinates in both radians and degrees. Negative values are acceptable.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between atan and atan2?
A: atan2(y,x) considers the signs of both coordinates to determine the correct quadrant, while atan(y/x) only returns values between -π/2 and π/2.

Q2: How are negative coordinates handled?
A: Negative x or y values will result in angles in the appropriate quadrant (e.g., second or third quadrant for negative x).

Q3: What's the range of θ in degrees?
A: The angle θ ranges from -180° to +180° (or equivalently 0° to 360° if adjusted).

Q4: Can I convert back to Cartesian coordinates?
A: Yes, using x = r·cos(θ) and y = r·sin(θ).

Q5: When would I use polar coordinates?
A: Common applications include antenna radiation patterns, circular motion analysis, and any system with radial symmetry.