This is the Best Answer for Identify the surface whose equation is given. (Spherical Coordinate Calculus)?
Multiply both sides by ρ:
==> ρ^2 = ρ sin θ sin φ.
Now, we can directly convert to rectangular coordinates:
x^2 + y^2 + z^2 = y, which is a sphere.
To get this into standard form, complete the square:
x^2 + (y^2 - y) + z^2 = 0
==> x^2 + (y^2 - y + 1/4) + z^2 = 1/4
==> x^2 + (y - 1/2)^2 + z^2 = (1/2)^2, which has center (0, 1/2, 0) and radius 1/2.
I hope this helps!