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!
Lorem ipsum dolor sit amet, consectetur adipiscing elit,
sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam,
quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor
in reprehenderit in voluptate velit esse cillum dolore eu fugiat.
SHOW ANSWER