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 when working with different coordinate systems.

2. How Does the Calculator Work?

The calculator uses the conversion equations:

Where:

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

Explanation: The equations project the polar coordinates onto the Cartesian plane using trigonometric functions.

3. Importance of Coordinate Conversion

Details: Coordinate conversion is essential for solving problems in different contexts where one coordinate system may be more convenient than another, such as in graphics programming or physics simulations.

4. Using the Calculator

Tips: Enter the radius (r) and angle (θ) in radians. The calculator will provide the corresponding Cartesian (x, y) coordinates.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between polar and Cartesian coordinates?
A: Polar uses radius and angle (r, θ), while Cartesian uses horizontal and vertical distances (x, y).

Q2: How do I convert degrees to radians?
A: Multiply degrees by π/180 (approximately 0.0174533).

Q3: Can r be negative in polar coordinates?
A: Yes, negative r values represent points in the opposite direction of the angle θ.

Q4: What's the range for θ?
A: Typically 0 to 2π radians (0° to 360°), but angles outside this range are valid.

Q5: When would I use polar coordinates?
A: Polar coordinates are often used in circular/rotational systems, like antenna radiation patterns or circular motion problems.