1. What is a Cylindrical Graph?

A cylindrical graph represents a three-dimensional function in cylindrical coordinates (r, θ, z), where r is the radial distance from the origin, θ is the angle from a reference direction, and z is the height above the reference plane.

2. How Does the Calculator Work?

The calculator plots the function:

Where:

• \( r \) — Radial distance from origin (units)
• \( \theta \) — Angle from reference direction (radians)
• \( z \) — Height above reference plane (units)

Explanation: The calculator evaluates the function over the specified ranges of θ and z to generate a 3D surface plot.

3. Understanding Cylindrical Coordinates

Details: Cylindrical coordinates are useful for problems with symmetry about an axis, such as pipes, cylinders, or helical structures.

4. Using the Calculator

Tips: Enter your function using θ for angle and z for height. Common functions include:

• Simple cylinder: 2 (constant radius)
• Spiral: theta
• Wave pattern: sin(theta)+z

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between cylindrical and spherical coordinates?
A: Cylindrical uses (r, θ, z) while spherical uses (ρ, θ, φ). Cylindrical is better for cylinder-symmetric problems.

Q2: How do I convert between cylindrical and Cartesian coordinates?
A: x = r·cos(θ), y = r·sin(θ), z remains the same.

Q3: What are some common cylindrical functions?
A: Common patterns include helices (r = aθ + b), cones (r = kz), and waves (r = sin(θ) + cos(z)).

Q4: Why is my graph not showing?
A: Check your function syntax and ensure θ and z ranges are valid (θ typically 0-2π or 0-6.28).

Q5: Can I plot multiple functions?
A: This calculator plots one function at a time. For multiple plots, you would need to combine them into a single function.