1. What Are Polar Coordinates?

Polar coordinates represent points in a plane using a distance (r) from a reference point (pole) and an angle (θ) from a reference direction (polar axis). This system is particularly useful for circular and spiral patterns.

2. How Does Polar Plotting Work?

The polar plotting system uses these equations to convert to Cartesian coordinates:

Where:

• \( r \) — Radial distance from origin
• \( \theta \) — Angle from polar axis (usually in degrees)
• \( x \) — Horizontal Cartesian coordinate
• \( y \) — Vertical Cartesian coordinate

3. Converting Between Polar and Cartesian

Details: The calculator automatically converts your polar coordinates (r, θ) to Cartesian (x, y) coordinates. You can also plot polar equations like spirals, circles, and roses.

4. Using the Calculator

Tips: Enter the radius (r) and angle (θ in degrees). For advanced plotting, enter a polar equation like "r = 2*sin(3θ)" to see beautiful polar graphs.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between polar and Cartesian coordinates?
A: Cartesian uses (x,y) grid coordinates while polar uses (r,θ) distance and angle measurements.

Q2: Can I plot multiple points or equations?
A: Yes, separate multiple equations with semicolons in the equation field.

Q3: What are common polar equations?
A: Circles (r = a), spirals (r = aθ), cardioids (r = a(1 ± cosθ)), and roses (r = a cos(kθ)).

Q4: How do negative radii work in polar coordinates?
A: A negative radius means plot the point in the opposite direction of the angle.

Q5: Can I save or export my graph?
A: Right-click on the graph to copy the image or use Desmos screenshot tools.