1. What is Polar to Rectangular Conversion?

The polar to rectangular conversion transforms coordinates from the polar system (r, θ) to the rectangular 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 the conversion equations:

Where:

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

Explanation: The equations project the polar coordinates onto the x and y axes 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 electromagnetics, robotics, or computer graphics.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

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

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

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

Q4: What's the rectangular equivalent of θ = π/2?
A: For any r, θ = π/2 gives (0, r) since cos(π/2) = 0 and sin(π/2) = 1.

Q5: How is this used in real-world applications?
A: Used in antenna radiation patterns, orbital mechanics, and anywhere direction and magnitude are more natural than x,y coordinates.