Hypothetical 3 Dimensional Coordinates

[Leo Authersh]

If the coordinates

x = rsinθcosφ, y = rsinθsinφ, z = rcosθ

represent a Sphere, then what does the coordinates

x = rsinθcosφ, y = rsinθsinφ, z = rcosθsinφ

represent?

@fresh_42 @FactChecker @Infrared @WWGD

 

[Mark44]

If the coordinates

x = rsinθcosφ, y = rsinθsinφ, z = rcosθ

represent a Sphere

No, they don't. These are just the conversion formulas for converting from spherical coordinates to rectangular coordinates. (Although r should be $\rho$, the Greek letter rho.)

In spherical coordinates, the equation of a sphere is very simple: $\rho = k$.

, then what does the coordinates

x = rsinθcosφ, y = rsinθsinφ, z = rcosθsinφ

represent?

You might try combining the first and second equations (by squaring each side) and the second and third equations (doing the same thing), to get an equation in x,y, and z alone.

Mod note: Thread moved, as this is more of a general question than one concerned with topology or analysis.