1. What is Polar to Rectangular Conversion?

Polar to rectangular conversion transforms coordinates from polar (r, θ) to rectangular (x, y) form. This is essential in mathematics, physics, engineering, and computer graphics where different coordinate systems are used for different applications.

2. How Does the Calculator Work?

The calculator uses the conversion formulas:

Where:

• \( r \) — Magnitude (distance from origin)
• \( \theta \) — Angle in radians (measured from positive x-axis)
• \( x \) — Horizontal coordinate
• \( y \) — Vertical coordinate

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

3. Importance of Coordinate Conversion

Details: Many physical systems are easier to model in polar coordinates (like circular motion), while rectangular coordinates are better for vector operations and computer displays. Converting between them is fundamental in many fields.

4. Using the Calculator

Tips: Enter the magnitude (must be ≥0) and angle in radians. For degrees, first convert to radians (multiply by π/180). The calculator will output the corresponding x and y coordinates.

5. Frequently Asked Questions (FAQ)

Q1: Can I input angles in degrees?
A: The calculator requires radians. Convert degrees to radians first: radians = degrees × (π/180).

Q2: What's the range for θ?
A: Theta can be any real number as trigonometric functions are periodic (2π radians = 360°).

Q3: What if r is negative?
A: Magnitude should be ≥0. Negative r values would represent the point in the opposite direction (θ+π).

Q4: How precise are the results?
A: Results are rounded to 4 decimal places. Internal calculations use higher precision.

Q5: When would I need this conversion?
A: Common in antenna radiation patterns, complex numbers, orbital mechanics, and any system with rotational symmetry.