There are different ways to describe points in space. Here we demonstrate the three most common ways:
| Coordinate System |
Explanation and Domain Restrictions |
Rectangular Coordinates (Cartesian Coordinates)
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A point in rectangular or Cartesian coordinates is given by (x,y,z).
- x is the distance from the zy-plane.
- y is the distance from the xz-plane.
- z is the distance from the xy-plane.
x, y, and z can be any real numbers.
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Cylindrical Coordinates
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A point in cylindrical coordinates is given by (r,θ,z).
- r is the distance from the z-axis to the point.
r cannot be negative.
- θ, spelled 'theta' and pronounced 'thay tuh' or 'thee tuh', is the angle from the x-axis to the projection of the vector connecting the origin and point onto the xy-plane.
θ must be in the interval [0,2π).
- z is the distance between the point and the xy-plane.
z can be any real number.
Note that some texts do not place restrictions on the values of r and θ.
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Spherical Coordinates
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A point in spherical coordinates is given by (ρ,θ,φ).
- ρ, spelled 'rho' and pronounced 'row', is the distance from the point to the origin.
ρ cannot be negative.
- θ, spelled 'theta' and pronounced 'thay tuh', is the angle from the x-axis to the projection of the vector connecting the origin and point onto the xy-plane.
θ must be in the interval [0,2π).
- φ, spelled 'phi' and pronounced 'fee' or 'fie', is the angle between the vector and the z-axis.
φ must be in the interval [0,π].
Note that some texts do not place restrictions on the values of ρ, θ, and φ.
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