Solved: The view of the trefoil knot shown in Figure 8 is accurate, but it doesnt reveal

Chapter 13, Problem 42

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The view of the trefoil knot shown in Figure 8 is accurate, but it doesnt reveal the whole story. Use the parametric equations to sketch the curve by hand as viewed from above, with gaps indicating where the curve passes over itself. Start by showing that the projection of the curve onto the -plane has polar coordinates and , so varies between 1 and 3. Then show that has maximum and minimum values when the projection is halfway between and . ; When you have finished your sketch, use a computer to draw the curve with viewpoint directly above and compare with your sketch. Then use the computer to draw the curve from several other viewpoints. You can get a better impression of the curve if you plot a tube with radius 0.2 around the curve. (Use the tubeplot command in Maple.)