1. What is a Polar Equation?

A polar equation is a mathematical relationship expressed in polar coordinates, where each point is determined by a distance from a reference point (r) and an angle from a reference direction (θ). The general form is r = f(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 computes the radial distance r for a given angle θ based on the specified polar function.

3. Importance of Polar Equations

Details: Polar equations are essential for describing curves and shapes that are naturally circular or rotational, such as spirals, roses, and circles. They are widely used in physics, engineering, and computer graphics.

4. Using the Calculator

Tips: Enter the angle θ in radians. The calculator will compute the corresponding radial distance r based on the predefined polar function.

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 polar to Cartesian coordinates?
A: Use x = r·cosθ and y = r·sinθ to convert polar coordinates (r, θ) to Cartesian coordinates (x, y).

Q3: Can I plot polar equations?
A: Yes, polar equations can be plotted on polar graph paper or using software that supports polar coordinates.

Q4: What is the range of θ?
A: Typically, θ ranges from 0 to 2π radians (0° to 360°) for a complete plot, but it can extend beyond.

Q5: Are polar equations used in real life?
A: Yes, they are used in antenna design, orbital mechanics, and any field involving rotational symmetry.