- For spherical coordinate system x,y,z are used for reference. Imagine a sphere of radius 'r' with center at origin. Any point on the sphere is at the same distance 'r' from origin, therefore the spherical surface is defined as r = constant surface.
- Now consider a line from origin making angle θ with z-axis. Rotate this line about z-axis fixing the end at the origin. This forms a cone with angle θ. This conical surface is defined as θ= constant surface.
- When a sphere with center at origin intersects with a vertical cone with vertex at origin the intersection is a horizontal circle with radius equal to rsinθ.
- To locate a point in spherical co-ordinate system. Imagine Φ=constant plane. A horizontal circle with center on z-axis intersects Φ=constant plane. the intersection is a point.
Point in spherical system = (r, θ ,Φ)
In spherical system variation of angle θ is from 0 to 180 deg and variation of Φ is from 0 to 360 deg.
Cartesian from spherical
x = rsinθcosΦ
y = rsinθsinΦ
z = rcosθ
Spherical from Cartesian coordinates