# Polar Coordinates System

The relation between Cartesian coordinate system (x, y, z) and polar coordinate system (r, J, j) is give below:

The relation is as follows:
x = r sin J cos j
y = r sin J sin j
z = r cos J
and the volume element dV is:

dV = r² sin J dJ dj

where coordinate r shows distance between the origin point and point in question, J is the angle between r and z-axis and j is the angle between x-axis and r-projection on xy-plane. The polar coordinates are defined in the following region:

0 £ r £ ¥, 0 £ J £ p, 0 £ j £ 2p

where we can define all points unambiguously.