Calc 3 Spherical Coordinates

z in spherical

z = ρcosφ

x in spherical

x = ρsinφcosθ

y in spherical

y = ρsinφsinθ

horizontal plane

ρ = asecφ

xy-plane in spherical

φ= π/2

cone in spherical

φ= a

vertical half plane in spherical

θ = a

sphere centered at origin, radius a

ρ = a

dV in spherical

dV = (ρ^2)sinφdρdφdθ

x^2 + y^2 + z^2 = a

ρ^2 = a