[SOLVED] Identify the surface whose equation is given. (Spherical Coordinate Calculus)?

Question

Identify the surface whose equation is given. (Spherical Coordinate Calculus)?

Identify the surface when given:

ρ = sin θ sin φ

I'm having trouble figuring this out. The only thing that looks like it might be close to something is the fact that y = ρ sinθ sin φ, but even then I am not sure how to identify the surface that way.

The answers are in that image link.

Thanks for the help, guys!

Answer 1

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!

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