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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 (5t) in the spherical coordinates. 1. Change m to see the surface grow. It stops growing at m =? 2. Change n to see the surface grow. It stops growing at n =? 3. From 1 and 2, what is the domain for s and t of the function R(t) = sin (5t)? 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 find the general rule for the domain for s and t of the function R(t) = sin(kt).