Cylindrical coordinate system Totally Explained

Everything about Cylindrical Coordinates totally explained

The cylindrical coordinate system is a three-dimensional coordinate system which essentially extends circular polar coordinates by adding a third coordinate (usually denoted

z

) which measures the height of a point above the plane.
The notation for this coordinate system isn't uniform. The Standard ISO 31-11 establishes them as

(
ho,varphi,z)

. Nevertheless, in many cases the azimuth

varphi

is denoted as

heta

. Also, the radial coordinate is called

r

while the vertical coordinate is sometimes referred as

h

.
A point P is given as

(
ho, varphi, z)

. In terms of the Cartesian coordinate system:

$ho$ is the distance from O to P', the orthogonal projection of the point P onto the XY plane. This is the same as the distance of P to the z-axis.
$varphi$ is the angle between the positive x-axis and the line OP', measured counterclockwise.
$z$ is the same as the Cartesian coordinate $z$ .

Thus, the conversion function

f

from Cartesian coordinates to cylindrical coordinates is

f(
ho,varphi,z)=(sqrt,dk

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