1. What are Cylindrical Coordinates?

Cylindrical coordinates are a three-dimensional coordinate system that extends polar coordinates by adding a height coordinate (z). A point is represented as (r, φ, z), where r is the radial distance, φ is the azimuthal angle, and z is the height.

2. How Does the Calculator Work?

The calculator converts cylindrical coordinates to Cartesian coordinates using the formulas:

Where:

• \( r \) — Radial distance from z-axis (≥0)
• \( \phi \) — Azimuthal angle measured from positive x-axis (radians)
• \( z \) — Height coordinate

Explanation: The calculator takes cylindrical coordinates and computes the equivalent Cartesian coordinates (x, y, z).

3. Applications of Cylindrical Coordinates

Details: Cylindrical coordinates are particularly useful in problems involving symmetry about an axis, such as in electromagnetism, fluid dynamics, and engineering applications involving pipes, cylinders, or rotational systems.

4. Using the Calculator

Tips: Enter the radial distance (r ≥ 0), azimuthal angle in radians (φ), and height (z). The calculator will output the equivalent Cartesian coordinates (x, y, z).

5. Frequently Asked Questions (FAQ)

Q1: What is the range for the angle φ?
A: The angle φ is typically measured in radians and can range from 0 to 2π (0° to 360°), though it can extend beyond this range.

Q2: Can r be negative?
A: No, the radial distance r must be non-negative (r ≥ 0) as it represents a distance from the origin.

Q3: How do I convert degrees to radians?
A: Multiply degrees by π/180. For example, 180° = π radians, 90° = π/2 radians.

Q4: What are common applications of cylindrical coordinates?
A: They are widely used in physics, engineering, and computer graphics for problems with cylindrical symmetry.

Q5: Can this calculator handle reverse conversion?
A: This calculator specifically converts cylindrical to Cartesian coordinates. For the reverse conversion, a different calculator would be needed.