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:
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!