1. What is Polar to Rectangular Conversion?

The polar to rectangular conversion transforms coordinates from the polar system (r, θ) to the Cartesian system (x, y). This is essential in mathematics, physics, and engineering when working with different coordinate systems.

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 x and y axes using trigonometric functions.

3. Importance of Coordinate Conversion

Details: Many physical systems are easier to analyze in one coordinate system than another. Converting between systems allows choosing the most convenient representation for a given problem.

4. Using the Calculator

Tips: Enter the magnitude (r ≥ 0) and angle in radians. Remember that 2π radians = 360°. Negative angles represent clockwise rotation.

5. Frequently Asked Questions (FAQ)

Q1: How do I convert degrees to radians?
A: Multiply degrees by π/180. Many calculators have a degree-to-radian conversion function.

Q2: What if my angle is greater than 2π?
A: The calculator will give correct results as trigonometric functions are periodic with period 2π.

Q3: Can r be negative?
A: While mathematically possible, this calculator requires r ≥ 0 as negative magnitudes are uncommon in practical applications.

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

Q5: When would I use polar coordinates?
A: Polar coordinates are often used for circular or spiral patterns, antenna radiation patterns, and problems with central symmetry.