Cylindrical and spherical coordinates are two different systems for representing points in three-dimensional space. Cylindrical coordinates use a combination of distance from the origin, angle from a reference axis, and height above a reference plane. Spherical coordinates use a combination of distance from the origin, angle from a reference axis, and angle from a reference plane.
The main difference between cylindrical and spherical coordinates is the reference planes used. Cylindrical coordinates use a flat reference plane, while spherical coordinates use a curved reference plane. This leads to differences in the equations used to convert between the two coordinate systems.
Cylindrical coordinates are most commonly used in situations where the shape of an object is best described using circular or cylindrical shapes, such as in cylindrical tanks or pipes.
Spherical coordinates are most commonly used in situations where the shape of an object is best described using spherical shapes, such as in celestial objects like planets and stars.
To convert from cylindrical coordinates to spherical coordinates, use the equations r = √(x² + y²), θ = arctan(y/x), and φ = arccos(z/√(x² + y² + z²)). To convert from spherical coordinates to cylindrical coordinates, use the equations ρ = r*sin(φ), θ = θ, and z = r*cos(φ).