Exploring Spherical Coordinates
Spherical Coordinates: x = r(t) cos(t) sin(s), y = r(t) sin(t) sin(s), z = r(t) cos (s)
Below is the graph of the function r(t) = sin (t) in the spherical coordinates.
1. Change n to see the surface grow. It stops growing at n =?
2. Set n = 2. Change m to see the surface grow. It stops growing at m =?
3. From 1 and 2, what is the domain for s and t of the function r(t) = sin (t)?
4. Now set k = 2 to get r(t) = sin (2t). Repeat Step 1 and 2. Do you get the same answers.
5. Try several values of k and the general rule for the domain for s and t of the function r(t) = sin(kt).