About Cylindrical Coordinates

Cylindrical coordinates are a three-dimensional coordinate system that extends polar coordinates by adding a third coordinate (z) that measures the height above the xy-plane.

Key Concepts:

• r: Radial distance from the z-axis
• θ: Angle from the positive x-axis in the xy-plane
• z: Height above the xy-plane

Conversion Formulas:

• Cartesian to Cylindrical:
  • r = √(x² + y²)
  • θ = arctan(y/x)
  • z = z
• Cylindrical to Cartesian:
  • x = r cos(θ)
  • y = r sin(θ)
  • z = z

Applications:

• Physics and engineering problems with cylindrical symmetry
• Fluid dynamics and heat transfer
• Electromagnetic field calculations
• 3D modeling and computer graphics

Tips:

• r is always non-negative
• θ is typically measured in radians
• z can be positive or negative
• Be careful with the quadrant when calculating θ