Find parametric equations for the sphere centered at the origin and with radius 3. Use the parameters s and t in your answer.

Radius, r = 3

The equation of a sphere entered at the origin in cartesian coordinates is

x^2 + y^2 + z^2 = r^2

That in spherical coordinates is:

x = rcos (theta) * sin (phi)

y = r sin (theta) * sin (phi)

z = rcos (phi)

where you can make u = r cos (phi) to obtain the parametrical equations

x = √[r^2 - u^2] cos (theta)

y = √[r^2 - u^2] sin (theta)

z = u

where theta goes from 0 to 2π and u goes from - r to r.

In our case r = 3, so the parametrical equations are:

Answer:

x = √[9 - u^2] cos (theta)

y = √[9 - u^2] sin (theta)

z = u