Spherical and Cylindrical Coordinates
Spherical Coordinates
Conversion of Cartesian coordinates to polar coordinates can be expressed as
r = (x2 + y2 + z2)1/2 (1)
tan(Φ) = y / x (1a)
cos(Φ) = z / r
= z / (x2 + y2 + z2)1/2 (1b)
Conversion of polar coordinates to Cartesian coordinates can be expressed as
x = r cos(Φ) sin(θ) (2)
y = r sin(Φ) sin(θ) (2a)
z = r cos(θ) (2b)
Cylindrical Coordinates
Conversion of Cartesian coordinates to cylindrical coordinates for a point P can be expressed as
ρ = (x2 + y2)1/2 (3)
tan(Φ) = y / x (3a)
z = z (3b)
Conversion of cylindrical coordinates to Cartesian coordinates can be expressed as
x = ρ cos(Φ) (4)
y = ρ sin(Φ) (4b)
z = z (4c)
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