For a constant \(c\) in spherical coordinates \( (\rho,\theta,\phi)\), find the shape described by the equation \(\phi = c\)

(A) Line

(B) Circle

(C) Plane

(D) Sphere

(E) Cylinder

(F) Cone

Mathulator Apr 12, 2020

#1**0 **

Because of the spherical coordinates, phi = c traces a cylinder. So the answer is (E) cylinder.

Guest Apr 13, 2020

#2**0 **

In spherical coordinates, the \(\phi\) represents the angle between (the line segment between the origin and a point) and the x-y plane.

If \(\phi = c\), that means the angle \(\phi\) is constant. Construct a line L such that the angle between L and the x-y plane is \(\phi\), then revolve it around the z-axis. For any line segment L_{0 }in the resulting figure, the angle between L_{0} and x-y plane is \(\phi\). Therefore the resulting figure is a **cone**.

Therefore the answer is (F).

MaxWong Apr 14, 2020