1. What is Polar to Rectangular Conversion?

Polar to rectangular conversion transforms coordinates from the polar coordinate system (using radius and angle) to the Cartesian coordinate system (using x and y coordinates). This is essential in mathematics, physics, engineering, and computer graphics.

2. How Does the Calculator Work?

The calculator uses the standard conversion formulas:

Where:

• \( r \) — Radius or distance from origin
• \( \theta \) — Angle measured counterclockwise from positive x-axis
• \( x \) — Horizontal coordinate in Cartesian system
• \( y \) — Vertical coordinate in Cartesian system

Explanation: The formulas use trigonometric functions to convert polar coordinates (r, θ) to rectangular coordinates (x, y) based on the geometric relationships in a right triangle.

3. Importance of Coordinate Conversion

Details: Coordinate conversion is crucial for solving problems in multiple coordinate systems, analyzing vector quantities, computer graphics rendering, navigation systems, and electrical engineering applications involving phasors.

4. Using the Calculator

Tips: Enter radius as a non-negative value and angle in radians. For degrees, convert to radians first (multiply by π/180). The calculator provides precise x and y coordinates in the Cartesian plane.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between polar and rectangular coordinates?
A: Polar coordinates use distance and angle (r, θ), while rectangular coordinates use horizontal and vertical distances (x, y) from a fixed origin.

Q2: Can I use degrees instead of radians?
A: This calculator requires radians. Convert degrees to radians by multiplying by π/180 (approximately 0.0174533).

Q3: What are typical applications of polar to rectangular conversion?
A: Common applications include antenna radiation patterns, complex number calculations, computer graphics, robotics navigation, and signal processing.

Q4: How do I convert back from rectangular to polar coordinates?
A: Use the formulas: \( r = \sqrt{x^2 + y^2} \) and \( \theta = \arctan(y/x) \) with quadrant adjustments.

Q5: What is the range of valid angle values?
A: Angles can be any real number, but typically range from 0 to 2π radians (0° to 360°) for principal values.