Imagine you're in a Geography professor's office and there is a globe in front of you. Suppose you put a pen at the North Pole, start spinning the globe, and then you slowly move the pen from the North Pole to the South Pole. You would get a picture that looks like this: 0 . 5 -0 . 5 -0.5 0.5 Try to replicate this picture as closely as possible. You should turn in your parametrization, with the commanding graph, and an explanation of how you arrived at your answer. Simply stumbling across the correct answer will result in little credit. You may use the following hints: Every point on this curve is on the unit sphere x2+ y + 22 = 1, so when you think you have your final parametrization, you should make sure that if you square x(t), y(t), and z(t), and add them all together you'll get 1. There are many possible parametrizations, but in the one originally used to create this picture, z(t)=Cos[n't] and t goes from 0 to 1. Seen from the top down, the path makes twenty revolutions around the sphere. So you could start by parametrizationich makes 20 revolutions and has the z(t) component given above. Then decide how to change x(t) and y(t). (Extra hint: you multiply them by the same thing, something which goes from 0 to 1 and back to 0 again as t goes from 0 to 1 itself.)