1. What is a Polar Equation?

A polar equation defines a relationship between the radial distance r and the angle θ (theta) in polar coordinates. Unlike Cartesian coordinates which use (x,y), polar coordinates represent points as (r,θ).

2. How Does the Calculator Work?

The calculator evaluates polar equations of the form:

Where:

• \( r \) — Radial distance from origin
• \( \theta \) — Angle in radians from polar axis
• \( f(\theta) \) — Function defining the relationship

Explanation: The calculator substitutes the θ value into your equation and computes the corresponding r value.

3. Importance of Polar Coordinates

Details: Polar coordinates are essential for problems involving circular or rotational symmetry, common in physics, engineering, and navigation.

4. Using the Calculator

Tips: Enter your polar equation using θ as the variable (e.g., "2*sin(θ)"). Enter θ in radians. The calculator will compute the corresponding r value.

5. Frequently Asked Questions (FAQ)

Q1: What are common polar equations?
A: Common examples include circles (r = a), cardioids (r = a(1 ± cosθ)), and spirals (r = aθ).

Q2: How do I convert between polar and Cartesian coordinates?
A: x = r·cosθ, y = r·sinθ. Conversely, r = √(x²+y²), θ = atan2(y,x).

Q3: Why use radians instead of degrees?
A: Radians are the natural unit for angle measurement in mathematics, simplifying many calculus operations.

Q4: Can I graph polar equations with this?
A: This calculator computes single points. For graphing, you would need to evaluate at multiple θ values.

Q5: What functions can I use in my equation?
A: Standard mathematical functions: sin, cos, tan, exp, log, etc. Use θ as your variable.