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 applications.

2. How Does the Calculator Work?

The calculator uses the conversion formulas:

Where:

• \( r \) — Radius (distance from origin)
• \( \theta \) — Angle in radians 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: Converting between coordinate systems is essential for solving problems in different contexts, as some problems are easier to solve in one system than another.

4. Using the Calculator

Tips: Enter radius (must be ≥0) and angle in radians. For degrees, first convert to radians (radians = degrees × π/180).

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: Can I input angle in degrees?
A: The calculator requires radians. Convert degrees to radians first by multiplying by π/180.

Q3: What's the range for θ?
A: The calculator accepts any real number for θ, as trigonometric functions are periodic.

Q4: What if my radius is negative?
A: The calculator requires r ≥ 0. Negative radii can be handled by adding π to θ.

Q5: When would I use polar coordinates?
A: Polar coordinates are often used for circular or spiral patterns, while rectangular is better for grid-like patterns.